Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.10 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.b.533.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.66046 | − | 0.492817i | −0.958668 | − | 0.284528i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.86278 | − | 1.23695i | 0.833060 | − | 0.553182i | ||||
\(6\) | −1.52260 | + | 0.825649i | −0.621598 | + | 0.337070i | ||||
\(7\) | −3.33681 | − | 3.33681i | −1.26119 | − | 1.26119i | −0.950515 | − | 0.310679i | \(-0.899444\pi\) |
−0.310679 | − | 0.950515i | \(-0.600556\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.51426 | + | 1.63661i | 0.838088 | + | 0.545536i | ||||
\(10\) | 0.442526 | − | 2.19184i | 0.139939 | − | 0.693121i | ||||
\(11\) | 0.00329918i | 0.000994740i | 1.00000 | 0.000497370i | \(0.000158318\pi\) | |||||
−1.00000 | 0.000497370i | \(0.999842\pi\) | ||||||||
\(12\) | −0.492817 | + | 1.66046i | −0.142264 | + | 0.479334i | ||||
\(13\) | 1.14909 | − | 1.14909i | 0.318700 | − | 0.318700i | −0.529568 | − | 0.848268i | \(-0.677646\pi\) |
0.848268 | + | 0.529568i | \(0.177646\pi\) | |||||||
\(14\) | −4.71896 | −1.26119 | ||||||||
\(15\) | −3.70266 | + | 1.13590i | −0.956024 | + | 0.293289i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.95340 | + | 4.95340i | −1.20138 | + | 1.20138i | −0.227627 | + | 0.973748i | \(0.573097\pi\) |
−0.973748 | + | 0.227627i | \(0.926903\pi\) | |||||||
\(18\) | 2.93511 | − | 0.620596i | 0.691812 | − | 0.146276i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −1.23695 | − | 1.86278i | −0.276591 | − | 0.416530i | ||||
\(21\) | 3.89620 | + | 7.18507i | 0.850221 | + | 1.56791i | ||||
\(22\) | 0.00233287 | + | 0.00233287i | 0.000497370 | + | 0.000497370i | ||||
\(23\) | −1.28904 | − | 1.28904i | −0.268783 | − | 0.268783i | 0.559826 | − | 0.828610i | \(-0.310868\pi\) |
−0.828610 | + | 0.559826i | \(0.810868\pi\) | |||||||
\(24\) | 0.825649 | + | 1.52260i | 0.168535 | + | 0.310799i | ||||
\(25\) | 1.93989 | − | 4.60834i | 0.387979 | − | 0.921668i | ||||
\(26\) | − | 1.62506i | − | 0.318700i | ||||||
\(27\) | −3.36829 | − | 3.95659i | −0.648227 | − | 0.761447i | ||||
\(28\) | −3.33681 | + | 3.33681i | −0.630597 | + | 0.630597i | ||||
\(29\) | 1.91798 | 0.356160 | 0.178080 | − | 0.984016i | \(-0.443011\pi\) | ||||
0.178080 | + | 0.984016i | \(0.443011\pi\) | |||||||
\(30\) | −1.81497 | + | 3.42138i | −0.331367 | + | 0.624656i | ||||
\(31\) | −3.49143 | −0.627079 | −0.313539 | − | 0.949575i | \(-0.601515\pi\) | ||||
−0.313539 | + | 0.949575i | \(0.601515\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0.00162589 | − | 0.00547816i | 0.000283031 | − | 0.000953625i | ||||
\(34\) | 7.00516i | 1.20138i | ||||||||
\(35\) | −10.3432 | − | 2.08826i | −1.74832 | − | 0.352980i | ||||
\(36\) | 1.63661 | − | 2.51426i | 0.272768 | − | 0.419044i | ||||
\(37\) | −6.71219 | − | 6.71219i | −1.10348 | − | 1.10348i | −0.993988 | − | 0.109488i | \(-0.965079\pi\) |
−0.109488 | − | 0.993988i | \(-0.534921\pi\) | |||||||
\(38\) | −0.707107 | − | 0.707107i | −0.114708 | − | 0.114708i | ||||
\(39\) | −2.47431 | + | 1.34173i | −0.396206 | + | 0.214848i | ||||
\(40\) | −2.19184 | − | 0.442526i | −0.346561 | − | 0.0699695i | ||||
\(41\) | − | 3.63777i | − | 0.568125i | −0.958806 | − | 0.284062i | \(-0.908318\pi\) | ||
0.958806 | − | 0.284062i | \(-0.0916823\pi\) | |||||||
\(42\) | 7.83564 | + | 2.32558i | 1.20907 | + | 0.358845i | ||||
\(43\) | 1.52133 | − | 1.52133i | 0.232001 | − | 0.232001i | −0.581526 | − | 0.813528i | \(-0.697544\pi\) |
0.813528 | + | 0.581526i | \(0.197544\pi\) | |||||||
\(44\) | 0.00329918 | 0.000497370 | ||||||||
\(45\) | 6.70792 | − | 0.0613876i | 0.999958 | − | 0.00915113i | ||||
\(46\) | −1.82298 | −0.268783 | ||||||||
\(47\) | −2.07305 | + | 2.07305i | −0.302386 | + | 0.302386i | −0.841947 | − | 0.539561i | \(-0.818590\pi\) |
0.539561 | + | 0.841947i | \(0.318590\pi\) | |||||||
\(48\) | 1.66046 | + | 0.492817i | 0.239667 | + | 0.0711320i | ||||
\(49\) | 15.2685i | 2.18122i | ||||||||
\(50\) | −1.88688 | − | 4.63030i | −0.266845 | − | 0.654824i | ||||
\(51\) | 10.6660 | − | 5.78381i | 1.49354 | − | 0.809895i | ||||
\(52\) | −1.14909 | − | 1.14909i | −0.159350 | − | 0.159350i | ||||
\(53\) | 5.97702 | + | 5.97702i | 0.821007 | + | 0.821007i | 0.986252 | − | 0.165245i | \(-0.0528416\pi\) |
−0.165245 | + | 0.986252i | \(0.552842\pi\) | |||||||
\(54\) | −5.17947 | − | 0.415995i | −0.704837 | − | 0.0566098i | ||||
\(55\) | 0.00408093 | + | 0.00614564i | 0.000550272 | + | 0.000828678i | ||||
\(56\) | 4.71896i | 0.630597i | ||||||||
\(57\) | −0.492817 | + | 1.66046i | −0.0652752 | + | 0.219933i | ||||
\(58\) | 1.35622 | − | 1.35622i | 0.178080 | − | 0.178080i | ||||
\(59\) | 11.8886 | 1.54776 | 0.773882 | − | 0.633330i | \(-0.218312\pi\) | ||||
0.773882 | + | 0.633330i | \(0.218312\pi\) | |||||||
\(60\) | 1.13590 | + | 3.70266i | 0.146645 | + | 0.478012i | ||||
\(61\) | −1.95331 | −0.250096 | −0.125048 | − | 0.992151i | \(-0.539908\pi\) | ||||
−0.125048 | + | 0.992151i | \(0.539908\pi\) | |||||||
\(62\) | −2.46881 | + | 2.46881i | −0.313539 | + | 0.313539i | ||||
\(63\) | −2.92857 | − | 13.8506i | −0.368965 | − | 1.74502i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.719129 | − | 3.56186i | 0.0891970 | − | 0.441795i | ||||
\(66\) | −0.00272396 | − | 0.00502332i | −0.000335297 | − | 0.000618328i | ||||
\(67\) | −5.56623 | − | 5.56623i | −0.680024 | − | 0.680024i | 0.279982 | − | 0.960005i | \(-0.409672\pi\) |
−0.960005 | + | 0.279982i | \(0.909672\pi\) | |||||||
\(68\) | 4.95340 | + | 4.95340i | 0.600688 | + | 0.600688i | ||||
\(69\) | 1.50514 | + | 2.77566i | 0.181198 | + | 0.334150i | ||||
\(70\) | −8.79037 | + | 5.83713i | −1.05065 | + | 0.697670i | ||||
\(71\) | − | 3.22989i | − | 0.383318i | −0.981462 | − | 0.191659i | \(-0.938613\pi\) | ||
0.981462 | − | 0.191659i | \(-0.0613867\pi\) | |||||||
\(72\) | −0.620596 | − | 2.93511i | −0.0731380 | − | 0.345906i | ||||
\(73\) | 10.3760 | − | 10.3760i | 1.21442 | − | 1.21442i | 0.244868 | − | 0.969556i | \(-0.421255\pi\) |
0.969556 | − | 0.244868i | \(-0.0787447\pi\) | |||||||
\(74\) | −9.49246 | −1.10348 | ||||||||
\(75\) | −5.49219 | + | 6.69596i | −0.634183 | + | 0.773183i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.0110087 | − | 0.0110087i | 0.00125456 | − | 0.00125456i | ||||
\(78\) | −0.800855 | + | 2.69834i | −0.0906790 | + | 0.305527i | ||||
\(79\) | − | 12.5069i | − | 1.40714i | −0.710625 | − | 0.703570i | \(-0.751588\pi\) | ||
0.710625 | − | 0.703570i | \(-0.248412\pi\) | |||||||
\(80\) | −1.86278 | + | 1.23695i | −0.208265 | + | 0.138296i | ||||
\(81\) | 3.64303 | + | 8.22972i | 0.404782 | + | 0.914413i | ||||
\(82\) | −2.57229 | − | 2.57229i | −0.284062 | − | 0.284062i | ||||
\(83\) | 9.29959 | + | 9.29959i | 1.02076 | + | 1.02076i | 0.999780 | + | 0.0209831i | \(0.00667960\pi\) |
0.0209831 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(84\) | 7.18507 | − | 3.89620i | 0.783955 | − | 0.425110i | ||||
\(85\) | −3.09997 | + | 15.3542i | −0.336238 | + | 1.66540i | ||||
\(86\) | − | 2.15149i | − | 0.232001i | ||||||
\(87\) | −3.18473 | − | 0.945213i | −0.341439 | − | 0.101338i | ||||
\(88\) | 0.00233287 | − | 0.00233287i | 0.000248685 | − | 0.000248685i | ||||
\(89\) | −6.59825 | −0.699413 | −0.349706 | − | 0.936859i | \(-0.613719\pi\) | ||||
−0.349706 | + | 0.936859i | \(0.613719\pi\) | |||||||
\(90\) | 4.69981 | − | 4.78663i | 0.495403 | − | 0.504555i | ||||
\(91\) | −7.66856 | −0.803884 | ||||||||
\(92\) | −1.28904 | + | 1.28904i | −0.134392 | + | 0.134392i | ||||
\(93\) | 5.79738 | + | 1.72063i | 0.601160 | + | 0.178421i | ||||
\(94\) | 2.93174i | 0.302386i | ||||||||
\(95\) | −1.23695 | − | 1.86278i | −0.126909 | − | 0.191117i | ||||
\(96\) | 1.52260 | − | 0.825649i | 0.155399 | − | 0.0842675i | ||||
\(97\) | 7.72270 | + | 7.72270i | 0.784121 | + | 0.784121i | 0.980523 | − | 0.196402i | \(-0.0629258\pi\) |
−0.196402 | + | 0.980523i | \(0.562926\pi\) | |||||||
\(98\) | 10.7965 | + | 10.7965i | 1.09061 | + | 1.09061i | ||||
\(99\) | −0.00539946 | + | 0.00829500i | −0.000542666 | + | 0.000833679i | ||||
\(100\) | −4.60834 | − | 1.93989i | −0.460834 | − | 0.193989i | ||||
\(101\) | − | 16.1869i | − | 1.61066i | −0.592826 | − | 0.805330i | \(-0.701988\pi\) | ||
0.592826 | − | 0.805330i | \(-0.298012\pi\) | |||||||
\(102\) | 3.45226 | − | 11.6318i | 0.341825 | − | 1.15172i | ||||
\(103\) | 0.233618 | − | 0.233618i | 0.0230191 | − | 0.0230191i | −0.695504 | − | 0.718523i | \(-0.744819\pi\) |
0.718523 | + | 0.695504i | \(0.244819\pi\) | |||||||
\(104\) | −1.62506 | −0.159350 | ||||||||
\(105\) | 16.1454 | + | 8.56478i | 1.57563 | + | 0.835837i | ||||
\(106\) | 8.45278 | 0.821007 | ||||||||
\(107\) | 13.2302 | − | 13.2302i | 1.27901 | − | 1.27901i | 0.337791 | − | 0.941221i | \(-0.390320\pi\) |
0.941221 | − | 0.337791i | \(-0.109680\pi\) | |||||||
\(108\) | −3.95659 | + | 3.36829i | −0.380723 | + | 0.324114i | ||||
\(109\) | − | 15.5455i | − | 1.48899i | −0.667628 | − | 0.744495i | \(-0.732690\pi\) | ||
0.667628 | − | 0.744495i | \(-0.267310\pi\) | |||||||
\(110\) | 0.00723128 | + | 0.00145997i | 0.000689475 | + | 0.000139203i | ||||
\(111\) | 7.83744 | + | 14.4532i | 0.743897 | + | 1.37184i | ||||
\(112\) | 3.33681 | + | 3.33681i | 0.315298 | + | 0.315298i | ||||
\(113\) | 0.674324 | + | 0.674324i | 0.0634351 | + | 0.0634351i | 0.738113 | − | 0.674678i | \(-0.235717\pi\) |
−0.674678 | + | 0.738113i | \(0.735717\pi\) | |||||||
\(114\) | 0.825649 | + | 1.52260i | 0.0773291 | + | 0.142604i | ||||
\(115\) | −3.99568 | − | 0.806715i | −0.372599 | − | 0.0752265i | ||||
\(116\) | − | 1.91798i | − | 0.178080i | ||||||
\(117\) | 4.76971 | − | 1.00850i | 0.440960 | − | 0.0932362i | ||||
\(118\) | 8.40651 | − | 8.40651i | 0.773882 | − | 0.773882i | ||||
\(119\) | 33.0570 | 3.03033 | ||||||||
\(120\) | 3.42138 | + | 1.81497i | 0.312328 | + | 0.165684i | ||||
\(121\) | 11.0000 | 0.999999 | ||||||||
\(122\) | −1.38120 | + | 1.38120i | −0.125048 | + | 0.125048i | ||||
\(123\) | −1.79276 | + | 6.04038i | −0.161647 | + | 0.544643i | ||||
\(124\) | 3.49143i | 0.313539i | ||||||||
\(125\) | −2.08671 | − | 10.9839i | −0.186641 | − | 0.982428i | ||||
\(126\) | −11.8647 | − | 7.72308i | −1.05699 | − | 0.688026i | ||||
\(127\) | 0.324072 | + | 0.324072i | 0.0287567 | + | 0.0287567i | 0.721339 | − | 0.692582i | \(-0.243527\pi\) |
−0.692582 | + | 0.721339i | \(0.743527\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −3.27586 | + | 1.77638i | −0.288423 | + | 0.156401i | ||||
\(130\) | −2.01012 | − | 3.02712i | −0.176299 | − | 0.265496i | ||||
\(131\) | 15.9941i | 1.39741i | 0.715409 | + | 0.698706i | \(0.246240\pi\) | ||||
−0.715409 | + | 0.698706i | \(0.753760\pi\) | |||||||
\(132\) | −0.00547816 | − | 0.00162589i | −0.000476812 | − | 0.000141516i | ||||
\(133\) | −3.33681 | + | 3.33681i | −0.289338 | + | 0.289338i | ||||
\(134\) | −7.87184 | −0.680024 | ||||||||
\(135\) | −11.1685 | − | 3.20385i | −0.961231 | − | 0.275743i | ||||
\(136\) | 7.00516 | 0.600688 | ||||||||
\(137\) | 4.73854 | − | 4.73854i | 0.404841 | − | 0.404841i | −0.475094 | − | 0.879935i | \(-0.657586\pi\) |
0.879935 | + | 0.475094i | \(0.157586\pi\) | |||||||
\(138\) | 3.02698 | + | 0.898394i | 0.257674 | + | 0.0764764i | ||||
\(139\) | 21.0400i | 1.78459i | 0.451454 | + | 0.892294i | \(0.350905\pi\) | ||||
−0.451454 | + | 0.892294i | \(0.649095\pi\) | |||||||
\(140\) | −2.08826 | + | 10.3432i | −0.176490 | + | 0.874160i | ||||
\(141\) | 4.46386 | − | 2.42059i | 0.375925 | − | 0.203850i | ||||
\(142\) | −2.28388 | − | 2.28388i | −0.191659 | − | 0.191659i | ||||
\(143\) | 0.00379104 | + | 0.00379104i | 0.000317023 | + | 0.000317023i | ||||
\(144\) | −2.51426 | − | 1.63661i | −0.209522 | − | 0.136384i | ||||
\(145\) | 3.57277 | − | 2.37245i | 0.296703 | − | 0.197021i | ||||
\(146\) | − | 14.6739i | − | 1.21442i | ||||||
\(147\) | 7.52460 | − | 25.3528i | 0.620618 | − | 2.09107i | ||||
\(148\) | −6.71219 | + | 6.71219i | −0.551738 | + | 0.551738i | ||||
\(149\) | 9.46498 | 0.775402 | 0.387701 | − | 0.921785i | \(-0.373269\pi\) | ||||
0.387701 | + | 0.921785i | \(0.373269\pi\) | |||||||
\(150\) | 0.851196 | + | 8.61832i | 0.0694999 | + | 0.703683i | ||||
\(151\) | −11.5421 | −0.939279 | −0.469639 | − | 0.882858i | \(-0.655616\pi\) | ||||
−0.469639 | + | 0.882858i | \(0.655616\pi\) | |||||||
\(152\) | −0.707107 | + | 0.707107i | −0.0573539 | + | 0.0573539i | ||||
\(153\) | −20.5609 | + | 4.34738i | −1.66225 | + | 0.351465i | ||||
\(154\) | − | 0.0155687i | − | 0.00125456i | ||||||
\(155\) | −6.50376 | + | 4.31873i | −0.522394 | + | 0.346889i | ||||
\(156\) | 1.34173 | + | 2.47431i | 0.107424 | + | 0.198103i | ||||
\(157\) | −8.81673 | − | 8.81673i | −0.703651 | − | 0.703651i | 0.261541 | − | 0.965192i | \(-0.415769\pi\) |
−0.965192 | + | 0.261541i | \(0.915769\pi\) | |||||||
\(158\) | −8.84374 | − | 8.84374i | −0.703570 | − | 0.703570i | ||||
\(159\) | −6.97903 | − | 12.8702i | −0.553473 | − | 1.02067i | ||||
\(160\) | −0.442526 | + | 2.19184i | −0.0349847 | + | 0.173280i | ||||
\(161\) | 8.60255i | 0.677976i | ||||||||
\(162\) | 8.39531 | + | 3.24328i | 0.659597 | + | 0.254816i | ||||
\(163\) | 1.80955 | − | 1.80955i | 0.141735 | − | 0.141735i | −0.632679 | − | 0.774414i | \(-0.718045\pi\) |
0.774414 | + | 0.632679i | \(0.218045\pi\) | |||||||
\(164\) | −3.63777 | −0.284062 | ||||||||
\(165\) | −0.00374755 | − | 0.0122158i | −0.000291746 | − | 0.000950995i | ||||
\(166\) | 13.1516 | 1.02076 | ||||||||
\(167\) | 10.1823 | − | 10.1823i | 0.787928 | − | 0.787928i | −0.193226 | − | 0.981154i | \(-0.561895\pi\) |
0.981154 | + | 0.193226i | \(0.0618952\pi\) | |||||||
\(168\) | 2.32558 | − | 7.83564i | 0.179423 | − | 0.604533i | ||||
\(169\) | 10.3592i | 0.796861i | ||||||||
\(170\) | 8.66506 | + | 13.0491i | 0.664580 | + | 1.00082i | ||||
\(171\) | 1.63661 | − | 2.51426i | 0.125154 | − | 0.192270i | ||||
\(172\) | −1.52133 | − | 1.52133i | −0.116001 | − | 0.116001i | ||||
\(173\) | −4.12383 | − | 4.12383i | −0.313529 | − | 0.313529i | 0.532746 | − | 0.846275i | \(-0.321160\pi\) |
−0.846275 | + | 0.532746i | \(0.821160\pi\) | |||||||
\(174\) | −2.92031 | + | 1.58358i | −0.221388 | + | 0.120051i | ||||
\(175\) | −21.8502 | + | 8.90409i | −1.65172 | + | 0.673086i | ||||
\(176\) | − | 0.00329918i | − | 0.000248685i | ||||||
\(177\) | −19.7406 | − | 5.85890i | −1.48379 | − | 0.440382i | ||||
\(178\) | −4.66567 | + | 4.66567i | −0.349706 | + | 0.349706i | ||||
\(179\) | −1.74920 | −0.130741 | −0.0653706 | − | 0.997861i | \(-0.520823\pi\) | ||||
−0.0653706 | + | 0.997861i | \(0.520823\pi\) | |||||||
\(180\) | −0.0613876 | − | 6.70792i | −0.00457556 | − | 0.499979i | ||||
\(181\) | −16.8570 | −1.25297 | −0.626485 | − | 0.779434i | \(-0.715507\pi\) | ||||
−0.626485 | + | 0.779434i | \(0.715507\pi\) | |||||||
\(182\) | −5.42249 | + | 5.42249i | −0.401942 | + | 0.401942i | ||||
\(183\) | 3.24339 | + | 0.962624i | 0.239759 | + | 0.0711592i | ||||
\(184\) | 1.82298i | 0.134392i | ||||||||
\(185\) | −20.8060 | − | 4.20066i | −1.52969 | − | 0.308839i | ||||
\(186\) | 5.31604 | − | 2.88269i | 0.389791 | − | 0.211369i | ||||
\(187\) | −0.0163421 | − | 0.0163421i | −0.00119506 | − | 0.00119506i | ||||
\(188\) | 2.07305 | + | 2.07305i | 0.151193 | + | 0.151193i | ||||
\(189\) | −1.96306 | + | 24.4417i | −0.142792 | + | 1.77787i | ||||
\(190\) | −2.19184 | − | 0.442526i | −0.159013 | − | 0.0321042i | ||||
\(191\) | − | 2.59256i | − | 0.187591i | −0.995591 | − | 0.0937954i | \(-0.970100\pi\) | ||
0.995591 | − | 0.0937954i | \(-0.0299000\pi\) | |||||||
\(192\) | 0.492817 | − | 1.66046i | 0.0355660 | − | 0.119833i | ||||
\(193\) | −1.18301 | + | 1.18301i | −0.0851547 | + | 0.0851547i | −0.748401 | − | 0.663246i | \(-0.769178\pi\) |
0.663246 | + | 0.748401i | \(0.269178\pi\) | |||||||
\(194\) | 10.9215 | 0.784121 | ||||||||
\(195\) | −2.94943 | + | 5.55994i | −0.211213 | + | 0.398155i | ||||
\(196\) | 15.2685 | 1.09061 | ||||||||
\(197\) | −7.67888 | + | 7.67888i | −0.547097 | + | 0.547097i | −0.925600 | − | 0.378503i | \(-0.876439\pi\) |
0.378503 | + | 0.925600i | \(0.376439\pi\) | |||||||
\(198\) | 0.00204746 | + | 0.00968345i | 0.000145506 | + | 0.000688173i | ||||
\(199\) | − | 8.22358i | − | 0.582954i | −0.956578 | − | 0.291477i | \(-0.905853\pi\) | ||
0.956578 | − | 0.291477i | \(-0.0941467\pi\) | |||||||
\(200\) | −4.63030 | + | 1.88688i | −0.327412 | + | 0.133422i | ||||
\(201\) | 6.49938 | + | 11.9857i | 0.458431 | + | 0.845403i | ||||
\(202\) | −11.4459 | − | 11.4459i | −0.805330 | − | 0.805330i | ||||
\(203\) | −6.39993 | − | 6.39993i | −0.449187 | − | 0.449187i | ||||
\(204\) | −5.78381 | − | 10.6660i | −0.404947 | − | 0.746772i | ||||
\(205\) | −4.49975 | − | 6.77637i | −0.314276 | − | 0.473282i | ||||
\(206\) | − | 0.330386i | − | 0.0230191i | ||||||
\(207\) | −1.13133 | − | 5.35064i | −0.0786331 | − | 0.371895i | ||||
\(208\) | −1.14909 | + | 1.14909i | −0.0796749 | + | 0.0796749i | ||||
\(209\) | 0.00329918 | 0.000228209 | ||||||||
\(210\) | 17.4727 | − | 5.36028i | 1.20573 | − | 0.369894i | ||||
\(211\) | 14.8721 | 1.02384 | 0.511920 | − | 0.859033i | \(-0.328934\pi\) | ||||
0.511920 | + | 0.859033i | \(0.328934\pi\) | |||||||
\(212\) | 5.97702 | − | 5.97702i | 0.410503 | − | 0.410503i | ||||
\(213\) | −1.59175 | + | 5.36311i | −0.109065 | + | 0.367474i | ||||
\(214\) | − | 18.7103i | − | 1.27901i | ||||||
\(215\) | 0.952091 | − | 4.71573i | 0.0649320 | − | 0.321610i | ||||
\(216\) | −0.415995 | + | 5.17947i | −0.0283049 | + | 0.352419i | ||||
\(217\) | 11.6502 | + | 11.6502i | 0.790868 | + | 0.790868i | ||||
\(218\) | −10.9923 | − | 10.9923i | −0.744495 | − | 0.744495i | ||||
\(219\) | −22.3425 | + | 12.1155i | −1.50977 | + | 0.818692i | ||||
\(220\) | 0.00614564 | − | 0.00408093i | 0.000414339 | − | 0.000275136i | ||||
\(221\) | 11.3838i | 0.765756i | ||||||||
\(222\) | 15.7619 | + | 4.67805i | 1.05787 | + | 0.313970i | ||||
\(223\) | −4.56460 | + | 4.56460i | −0.305668 | + | 0.305668i | −0.843227 | − | 0.537558i | \(-0.819347\pi\) |
0.537558 | + | 0.843227i | \(0.319347\pi\) | |||||||
\(224\) | 4.71896 | 0.315298 | ||||||||
\(225\) | 12.4194 | − | 8.41174i | 0.827963 | − | 0.560783i | ||||
\(226\) | 0.953638 | 0.0634351 | ||||||||
\(227\) | −8.94878 | + | 8.94878i | −0.593952 | + | 0.593952i | −0.938696 | − | 0.344745i | \(-0.887965\pi\) |
0.344745 | + | 0.938696i | \(0.387965\pi\) | |||||||
\(228\) | 1.66046 | + | 0.492817i | 0.109967 | + | 0.0326376i | ||||
\(229\) | − | 15.6381i | − | 1.03339i | −0.856169 | − | 0.516696i | \(-0.827162\pi\) | ||
0.856169 | − | 0.516696i | \(-0.172838\pi\) | |||||||
\(230\) | −3.39580 | + | 2.25494i | −0.223913 | + | 0.148686i | ||||
\(231\) | −0.0237048 | + | 0.0128543i | −0.00155966 | + | 0.000845748i | ||||
\(232\) | −1.35622 | − | 1.35622i | −0.0890400 | − | 0.0890400i | ||||
\(233\) | −11.5507 | − | 11.5507i | −0.756711 | − | 0.756711i | 0.219012 | − | 0.975722i | \(-0.429717\pi\) |
−0.975722 | + | 0.219012i | \(0.929717\pi\) | |||||||
\(234\) | 2.65958 | − | 4.08582i | 0.173862 | − | 0.267098i | ||||
\(235\) | −1.29737 | + | 6.42592i | −0.0846312 | + | 0.419181i | ||||
\(236\) | − | 11.8886i | − | 0.773882i | ||||||
\(237\) | −6.16363 | + | 20.7673i | −0.400371 | + | 1.34898i | ||||
\(238\) | 23.3749 | − | 23.3749i | 1.51517 | − | 1.51517i | ||||
\(239\) | −10.3774 | −0.671261 | −0.335631 | − | 0.941994i | \(-0.608949\pi\) | ||||
−0.335631 | + | 0.941994i | \(0.608949\pi\) | |||||||
\(240\) | 3.70266 | − | 1.13590i | 0.239006 | − | 0.0733223i | ||||
\(241\) | 14.4062 | 0.927988 | 0.463994 | − | 0.885838i | \(-0.346416\pi\) | ||||
0.463994 | + | 0.885838i | \(0.346416\pi\) | |||||||
\(242\) | 7.77817 | − | 7.77817i | 0.500000 | − | 0.500000i | ||||
\(243\) | −1.99337 | − | 15.4605i | −0.127875 | − | 0.991790i | ||||
\(244\) | 1.95331i | 0.125048i | ||||||||
\(245\) | 18.8865 | + | 28.4419i | 1.20661 | + | 1.81709i | ||||
\(246\) | 3.00352 | + | 5.53886i | 0.191498 | + | 0.353145i | ||||
\(247\) | −1.14909 | − | 1.14909i | −0.0731147 | − | 0.0731147i | ||||
\(248\) | 2.46881 | + | 2.46881i | 0.156770 | + | 0.156770i | ||||
\(249\) | −10.8586 | − | 20.0246i | −0.688137 | − | 1.26901i | ||||
\(250\) | −9.24230 | − | 6.29125i | −0.584535 | − | 0.397894i | ||||
\(251\) | 20.7089i | 1.30713i | 0.756869 | + | 0.653567i | \(0.226728\pi\) | ||||
−0.756869 | + | 0.653567i | \(0.773272\pi\) | |||||||
\(252\) | −13.8506 | + | 2.92857i | −0.872509 | + | 0.184482i | ||||
\(253\) | 0.00425277 | − | 0.00425277i | 0.000267370 | − | 0.000267370i | ||||
\(254\) | 0.458306 | 0.0287567 | ||||||||
\(255\) | 12.7142 | − | 23.9674i | 0.796193 | − | 1.50089i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.24360 | − | 7.24360i | 0.451843 | − | 0.451843i | −0.444123 | − | 0.895966i | \(-0.646485\pi\) |
0.895966 | + | 0.444123i | \(0.146485\pi\) | |||||||
\(258\) | −1.06029 | + | 3.57247i | −0.0660109 | + | 0.222412i | ||||
\(259\) | 44.7945i | 2.78340i | ||||||||
\(260\) | −3.56186 | − | 0.719129i | −0.220897 | − | 0.0445985i | ||||
\(261\) | 4.82231 | + | 3.13898i | 0.298493 | + | 0.194298i | ||||
\(262\) | 11.3095 | + | 11.3095i | 0.698706 | + | 0.698706i | ||||
\(263\) | 1.90123 | + | 1.90123i | 0.117235 | + | 0.117235i | 0.763290 | − | 0.646056i | \(-0.223583\pi\) |
−0.646056 | + | 0.763290i | \(0.723583\pi\) | |||||||
\(264\) | −0.00502332 | + | 0.00272396i | −0.000309164 | + | 0.000167648i | ||||
\(265\) | 18.5272 | + | 3.74058i | 1.13811 | + | 0.229782i | ||||
\(266\) | 4.71896i | 0.289338i | ||||||||
\(267\) | 10.9561 | + | 3.25173i | 0.670505 | + | 0.199003i | ||||
\(268\) | −5.56623 | + | 5.56623i | −0.340012 | + | 0.340012i | ||||
\(269\) | −21.4029 | −1.30496 | −0.652480 | − | 0.757806i | \(-0.726271\pi\) | ||||
−0.652480 | + | 0.757806i | \(0.726271\pi\) | |||||||
\(270\) | −10.1628 | + | 5.63186i | −0.618487 | + | 0.342744i | ||||
\(271\) | 4.88606 | 0.296807 | 0.148404 | − | 0.988927i | \(-0.452587\pi\) | ||||
0.148404 | + | 0.988927i | \(0.452587\pi\) | |||||||
\(272\) | 4.95340 | − | 4.95340i | 0.300344 | − | 0.300344i | ||||
\(273\) | 12.7334 | + | 3.77920i | 0.770657 | + | 0.228727i | ||||
\(274\) | − | 6.70131i | − | 0.404841i | ||||||
\(275\) | 0.0152037 | + | 0.00640005i | 0.000916820 | + | 0.000385938i | ||||
\(276\) | 2.77566 | − | 1.50514i | 0.167075 | − | 0.0905988i | ||||
\(277\) | 16.6272 | + | 16.6272i | 0.999031 | + | 0.999031i | 1.00000 | 0.000968978i | \(-0.000308435\pi\) | |
−0.000968978 | 1.00000i | \(0.500308\pi\) | ||||||||
\(278\) | 14.8775 | + | 14.8775i | 0.892294 | + | 0.892294i | ||||
\(279\) | −8.77836 | − | 5.71409i | −0.525547 | − | 0.342094i | ||||
\(280\) | 5.83713 | + | 8.79037i | 0.348835 | + | 0.525325i | ||||
\(281\) | − | 7.94326i | − | 0.473855i | −0.971527 | − | 0.236928i | \(-0.923860\pi\) | ||
0.971527 | − | 0.236928i | \(-0.0761404\pi\) | |||||||
\(282\) | 1.44481 | − | 4.86804i | 0.0860373 | − | 0.289888i | ||||
\(283\) | −8.91351 | + | 8.91351i | −0.529853 | + | 0.529853i | −0.920529 | − | 0.390675i | \(-0.872242\pi\) |
0.390675 | + | 0.920529i | \(0.372242\pi\) | |||||||
\(284\) | −3.22989 | −0.191659 | ||||||||
\(285\) | 1.13590 | + | 3.70266i | 0.0672851 | + | 0.219327i | ||||
\(286\) | 0.00536135 | 0.000317023 | ||||||||
\(287\) | −12.1385 | + | 12.1385i | −0.716515 | + | 0.716515i | ||||
\(288\) | −2.93511 | + | 0.620596i | −0.172953 | + | 0.0365690i | ||||
\(289\) | − | 32.0723i | − | 1.88661i | ||||||
\(290\) | 0.848756 | − | 4.20391i | 0.0498407 | − | 0.246862i | ||||
\(291\) | −9.01736 | − | 16.6291i | −0.528607 | − | 0.974816i | ||||
\(292\) | −10.3760 | − | 10.3760i | −0.607212 | − | 0.607212i | ||||
\(293\) | 14.7740 | + | 14.7740i | 0.863104 | + | 0.863104i | 0.991697 | − | 0.128593i | \(-0.0410462\pi\) |
−0.128593 | + | 0.991697i | \(0.541046\pi\) | |||||||
\(294\) | −12.6065 | − | 23.2478i | −0.735223 | − | 1.35584i | ||||
\(295\) | 22.1458 | − | 14.7056i | 1.28938 | − | 0.856196i | ||||
\(296\) | 9.49246i | 0.551738i | ||||||||
\(297\) | 0.0130535 | − | 0.0111126i | 0.000757441 | − | 0.000644817i | ||||
\(298\) | 6.69275 | − | 6.69275i | 0.387701 | − | 0.387701i | ||||
\(299\) | −2.96244 | −0.171322 | ||||||||
\(300\) | 6.69596 | + | 5.49219i | 0.386591 | + | 0.317092i | ||||
\(301\) | −10.1528 | −0.585197 | ||||||||
\(302\) | −8.16146 | + | 8.16146i | −0.469639 | + | 0.469639i | ||||
\(303\) | −7.97720 | + | 26.8778i | −0.458278 | + | 1.54409i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | −3.63858 | + | 2.41615i | −0.208345 | + | 0.138348i | ||||
\(306\) | −11.4647 | + | 17.6128i | −0.655393 | + | 1.00686i | ||||
\(307\) | −20.3918 | − | 20.3918i | −1.16382 | − | 1.16382i | −0.983632 | − | 0.180188i | \(-0.942329\pi\) |
−0.180188 | − | 0.983632i | \(-0.557671\pi\) | |||||||
\(308\) | −0.0110087 | − | 0.0110087i | −0.000627280 | − | 0.000627280i | ||||
\(309\) | −0.503045 | + | 0.272783i | −0.0286172 | + | 0.0155181i | ||||
\(310\) | −1.54505 | + | 7.65265i | −0.0877527 | + | 0.434642i | ||||
\(311\) | 6.29224i | 0.356800i | 0.983958 | + | 0.178400i | \(0.0570921\pi\) | ||||
−0.983958 | + | 0.178400i | \(0.942908\pi\) | |||||||
\(312\) | 2.69834 | + | 0.800855i | 0.152763 | + | 0.0453395i | ||||
\(313\) | 5.94003 | − | 5.94003i | 0.335750 | − | 0.335750i | −0.519015 | − | 0.854765i | \(-0.673701\pi\) |
0.854765 | + | 0.519015i | \(0.173701\pi\) | |||||||
\(314\) | −12.4687 | −0.703651 | ||||||||
\(315\) | −22.5879 | − | 22.1782i | −1.27268 | − | 1.24960i | ||||
\(316\) | −12.5069 | −0.703570 | ||||||||
\(317\) | −12.9036 | + | 12.9036i | −0.724736 | + | 0.724736i | −0.969566 | − | 0.244830i | \(-0.921268\pi\) |
0.244830 | + | 0.969566i | \(0.421268\pi\) | |||||||
\(318\) | −14.0355 | − | 4.16568i | −0.787073 | − | 0.233600i | ||||
\(319\) | 0.00632776i | 0.000354287i | ||||||||
\(320\) | 1.23695 | + | 1.86278i | 0.0691478 | + | 0.104133i | ||||
\(321\) | −28.4883 | + | 15.4482i | −1.59006 | + | 0.862233i | ||||
\(322\) | 6.08292 | + | 6.08292i | 0.338988 | + | 0.338988i | ||||
\(323\) | 4.95340 | + | 4.95340i | 0.275614 | + | 0.275614i | ||||
\(324\) | 8.22972 | − | 3.64303i | 0.457207 | − | 0.202391i | ||||
\(325\) | −3.06628 | − | 7.52450i | −0.170087 | − | 0.417384i | ||||
\(326\) | − | 2.55908i | − | 0.141735i | ||||||
\(327\) | −7.66110 | + | 25.8127i | −0.423660 | + | 1.42745i | ||||
\(328\) | −2.57229 | + | 2.57229i | −0.142031 | + | 0.142031i | ||||
\(329\) | 13.8348 | 0.762735 | ||||||||
\(330\) | −0.0112878 | − | 0.00598792i | −0.000621371 | − | 0.000329624i | ||||
\(331\) | −22.2824 | −1.22475 | −0.612376 | − | 0.790567i | \(-0.709786\pi\) | ||||
−0.612376 | + | 0.790567i | \(0.709786\pi\) | |||||||
\(332\) | 9.29959 | − | 9.29959i | 0.510381 | − | 0.510381i | ||||
\(333\) | −5.89099 | − | 27.8614i | −0.322824 | − | 1.52680i | ||||
\(334\) | − | 14.3999i | − | 0.787928i | ||||||
\(335\) | −17.2538 | − | 3.48349i | −0.942678 | − | 0.190324i | ||||
\(336\) | −3.89620 | − | 7.18507i | −0.212555 | − | 0.391978i | ||||
\(337\) | 19.0330 | + | 19.0330i | 1.03679 | + | 1.03679i | 0.999297 | + | 0.0374972i | \(0.0119385\pi\) |
0.0374972 | + | 0.999297i | \(0.488061\pi\) | |||||||
\(338\) | 7.32506 | + | 7.32506i | 0.398431 | + | 0.398431i | ||||
\(339\) | −0.787371 | − | 1.45201i | −0.0427641 | − | 0.0788622i | ||||
\(340\) | 15.3542 | + | 3.09997i | 0.832699 | + | 0.168119i | ||||
\(341\) | − | 0.0115188i | − | 0.000623780i | ||||||
\(342\) | −0.620596 | − | 2.93511i | −0.0335580 | − | 0.158712i | ||||
\(343\) | 27.5905 | − | 27.5905i | 1.48975 | − | 1.48975i | ||||
\(344\) | −2.15149 | −0.116001 | ||||||||
\(345\) | 6.23711 | + | 3.30866i | 0.335795 | + | 0.178132i | ||||
\(346\) | −5.83198 | −0.313529 | ||||||||
\(347\) | −2.64462 | + | 2.64462i | −0.141971 | + | 0.141971i | −0.774520 | − | 0.632549i | \(-0.782009\pi\) |
0.632549 | + | 0.774520i | \(0.282009\pi\) | |||||||
\(348\) | −0.945213 | + | 3.18473i | −0.0506688 | + | 0.170720i | ||||
\(349\) | 27.9124i | 1.49412i | 0.664758 | + | 0.747059i | \(0.268535\pi\) | ||||
−0.664758 | + | 0.747059i | \(0.731465\pi\) | |||||||
\(350\) | −9.15427 | + | 21.7466i | −0.489316 | + | 1.16240i | ||||
\(351\) | −8.41693 | − | 0.676015i | −0.449263 | − | 0.0360830i | ||||
\(352\) | −0.00233287 | − | 0.00233287i | −0.000124342 | − | 0.000124342i | ||||
\(353\) | 3.63692 | + | 3.63692i | 0.193574 | + | 0.193574i | 0.797238 | − | 0.603665i | \(-0.206293\pi\) |
−0.603665 | + | 0.797238i | \(0.706293\pi\) | |||||||
\(354\) | −18.1016 | + | 9.81581i | −0.962087 | + | 0.521705i | ||||
\(355\) | −3.99523 | − | 6.01658i | −0.212045 | − | 0.319327i | ||||
\(356\) | 6.59825i | 0.349706i | ||||||||
\(357\) | −54.8899 | − | 16.2911i | −2.90508 | − | 0.862215i | ||||
\(358\) | −1.23687 | + | 1.23687i | −0.0653706 | + | 0.0653706i | ||||
\(359\) | 19.0031 | 1.00295 | 0.501473 | − | 0.865173i | \(-0.332792\pi\) | ||||
0.501473 | + | 0.865173i | \(0.332792\pi\) | |||||||
\(360\) | −4.78663 | − | 4.69981i | −0.252277 | − | 0.247702i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −11.9197 | + | 11.9197i | −0.626485 | + | 0.626485i | ||||
\(363\) | −18.2651 | − | 5.42098i | −0.958667 | − | 0.284528i | ||||
\(364\) | 7.66856i | 0.401942i | ||||||||
\(365\) | 6.49360 | − | 32.1630i | 0.339891 | − | 1.68349i | ||||
\(366\) | 2.97410 | − | 1.61275i | 0.155459 | − | 0.0842997i | ||||
\(367\) | 3.36608 | + | 3.36608i | 0.175708 | + | 0.175708i | 0.789482 | − | 0.613774i | \(-0.210349\pi\) |
−0.613774 | + | 0.789482i | \(0.710349\pi\) | |||||||
\(368\) | 1.28904 | + | 1.28904i | 0.0671958 | + | 0.0671958i | ||||
\(369\) | 5.95360 | − | 9.14632i | 0.309932 | − | 0.476138i | ||||
\(370\) | −17.6824 | + | 11.7417i | −0.919262 | + | 0.610424i | ||||
\(371\) | − | 39.8883i | − | 2.07090i | ||||||
\(372\) | 1.72063 | − | 5.79738i | 0.0892107 | − | 0.300580i | ||||
\(373\) | 4.67503 | − | 4.67503i | 0.242064 | − | 0.242064i | −0.575640 | − | 0.817704i | \(-0.695247\pi\) |
0.817704 | + | 0.575640i | \(0.195247\pi\) | |||||||
\(374\) | −0.0231113 | −0.00119506 | ||||||||
\(375\) | −1.94814 | + | 19.2667i | −0.100602 | + | 0.994927i | ||||
\(376\) | 2.93174 | 0.151193 | ||||||||
\(377\) | 2.20393 | − | 2.20393i | 0.113508 | − | 0.113508i | ||||
\(378\) | 15.8948 | + | 18.6710i | 0.817540 | + | 0.960332i | ||||
\(379\) | 6.60335i | 0.339191i | 0.985514 | + | 0.169596i | \(0.0542461\pi\) | ||||
−0.985514 | + | 0.169596i | \(0.945754\pi\) | |||||||
\(380\) | −1.86278 | + | 1.23695i | −0.0955586 | + | 0.0634544i | ||||
\(381\) | −0.378400 | − | 0.697816i | −0.0193860 | − | 0.0357502i | ||||
\(382\) | −1.83322 | − | 1.83322i | −0.0937954 | − | 0.0937954i | ||||
\(383\) | 14.4355 | + | 14.4355i | 0.737619 | + | 0.737619i | 0.972117 | − | 0.234498i | \(-0.0753446\pi\) |
−0.234498 | + | 0.972117i | \(0.575345\pi\) | |||||||
\(384\) | −0.825649 | − | 1.52260i | −0.0421337 | − | 0.0776997i | ||||
\(385\) | 0.00688954 | − | 0.0341241i | 0.000351124 | − | 0.00173912i | ||||
\(386\) | 1.67302i | 0.0851547i | ||||||||
\(387\) | 6.31486 | − | 1.33521i | 0.321002 | − | 0.0678724i | ||||
\(388\) | 7.72270 | − | 7.72270i | 0.392061 | − | 0.392061i | ||||
\(389\) | −0.566176 | −0.0287063 | −0.0143531 | − | 0.999897i | \(-0.504569\pi\) | ||||
−0.0143531 | + | 0.999897i | \(0.504569\pi\) | |||||||
\(390\) | 1.84591 | + | 6.01703i | 0.0934711 | + | 0.304684i | ||||
\(391\) | 12.7703 | 0.645819 | ||||||||
\(392\) | 10.7965 | − | 10.7965i | 0.545305 | − | 0.545305i | ||||
\(393\) | 7.88217 | − | 26.5576i | 0.397603 | − | 1.33965i | ||||
\(394\) | 10.8596i | 0.547097i | ||||||||
\(395\) | −15.4705 | − | 23.2977i | −0.778405 | − | 1.17223i | ||||
\(396\) | 0.00829500 | + | 0.00539946i | 0.000416840 | + | 0.000271333i | ||||
\(397\) | 11.0271 | + | 11.0271i | 0.553436 | + | 0.553436i | 0.927431 | − | 0.373995i | \(-0.122012\pi\) |
−0.373995 | + | 0.927431i | \(0.622012\pi\) | |||||||
\(398\) | −5.81495 | − | 5.81495i | −0.291477 | − | 0.291477i | ||||
\(399\) | 7.18507 | − | 3.89620i | 0.359703 | − | 0.195054i | ||||
\(400\) | −1.93989 | + | 4.60834i | −0.0969947 | + | 0.230417i | ||||
\(401\) | − | 33.0910i | − | 1.65249i | −0.563313 | − | 0.826243i | \(-0.690474\pi\) | ||
0.563313 | − | 0.826243i | \(-0.309526\pi\) | |||||||
\(402\) | 13.0709 | + | 3.87938i | 0.651917 | + | 0.193486i | ||||
\(403\) | −4.01195 | + | 4.01195i | −0.199850 | + | 0.199850i | ||||
\(404\) | −16.1869 | −0.805330 | ||||||||
\(405\) | 16.9659 | + | 10.8239i | 0.843045 | + | 0.537843i | ||||
\(406\) | −9.05086 | −0.449187 | ||||||||
\(407\) | 0.0221447 | − | 0.0221447i | 0.00109767 | − | 0.00109767i | ||||
\(408\) | −11.6318 | − | 3.45226i | −0.575860 | − | 0.170912i | ||||
\(409\) | − | 26.2274i | − | 1.29686i | −0.761274 | − | 0.648430i | \(-0.775426\pi\) | ||
0.761274 | − | 0.648430i | \(-0.224574\pi\) | |||||||
\(410\) | −7.97342 | − | 1.60981i | −0.393779 | − | 0.0795028i | ||||
\(411\) | −10.2034 | + | 5.53293i | −0.503296 | + | 0.272919i | ||||
\(412\) | −0.233618 | − | 0.233618i | −0.0115095 | − | 0.0115095i | ||||
\(413\) | −39.6699 | − | 39.6699i | −1.95203 | − | 1.95203i | ||||
\(414\) | −4.58344 | − | 2.98350i | −0.225264 | − | 0.146631i | ||||
\(415\) | 28.8262 | + | 5.81993i | 1.41502 | + | 0.285689i | ||||
\(416\) | 1.62506i | 0.0796749i | ||||||||
\(417\) | 10.3689 | − | 34.9361i | 0.507765 | − | 1.71083i | ||||
\(418\) | 0.00233287 | − | 0.00233287i | 0.000114104 | − | 0.000114104i | ||||
\(419\) | 16.7418 | 0.817888 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(420\) | 8.56478 | − | 16.1454i | 0.417919 | − | 0.787813i | ||||
\(421\) | 20.3487 | 0.991734 | 0.495867 | − | 0.868399i | \(-0.334850\pi\) | ||||
0.495867 | + | 0.868399i | \(0.334850\pi\) | |||||||
\(422\) | 10.5162 | − | 10.5162i | 0.511920 | − | 0.511920i | ||||
\(423\) | −8.60498 | + | 1.81943i | −0.418389 | + | 0.0884636i | ||||
\(424\) | − | 8.45278i | − | 0.410503i | ||||||
\(425\) | 13.2179 | + | 32.4360i | 0.641162 | + | 1.57338i | ||||
\(426\) | 2.66676 | + | 4.91783i | 0.129205 | + | 0.238269i | ||||
\(427\) | 6.51781 | + | 6.51781i | 0.315419 | + | 0.315419i | ||||
\(428\) | −13.2302 | − | 13.2302i | −0.639506 | − | 0.639506i | ||||
\(429\) | −0.00442659 | − | 0.00816317i | −0.000213718 | − | 0.000394122i | ||||
\(430\) | −2.66129 | − | 4.00775i | −0.128339 | − | 0.193271i | ||||
\(431\) | − | 37.8255i | − | 1.82199i | −0.412418 | − | 0.910995i | \(-0.635316\pi\) | ||
0.412418 | − | 0.910995i | \(-0.364684\pi\) | |||||||
\(432\) | 3.36829 | + | 3.95659i | 0.162057 | + | 0.190362i | ||||
\(433\) | 3.73358 | − | 3.73358i | 0.179424 | − | 0.179424i | −0.611681 | − | 0.791105i | \(-0.709506\pi\) |
0.791105 | + | 0.611681i | \(0.209506\pi\) | |||||||
\(434\) | 16.4759 | 0.790868 | ||||||||
\(435\) | −7.10164 | + | 2.17864i | −0.340497 | + | 0.104458i | ||||
\(436\) | −15.5455 | −0.744495 | ||||||||
\(437\) | −1.28904 | + | 1.28904i | −0.0616631 | + | 0.0616631i | ||||
\(438\) | −7.23157 | + | 24.3655i | −0.345538 | + | 1.16423i | ||||
\(439\) | 9.80030i | 0.467743i | 0.972268 | + | 0.233871i | \(0.0751395\pi\) | ||||
−0.972268 | + | 0.233871i | \(0.924861\pi\) | |||||||
\(440\) | 0.00145997 | − | 0.00723128i | 6.96014e−5 | − | 0.000344738i | ||||
\(441\) | −24.9886 | + | 38.3891i | −1.18993 | + | 1.82805i | ||||
\(442\) | 8.04954 | + | 8.04954i | 0.382878 | + | 0.382878i | ||||
\(443\) | −7.47230 | − | 7.47230i | −0.355020 | − | 0.355020i | 0.506954 | − | 0.861973i | \(-0.330772\pi\) |
−0.861973 | + | 0.506954i | \(0.830772\pi\) | |||||||
\(444\) | 14.4532 | − | 7.83744i | 0.685919 | − | 0.371949i | ||||
\(445\) | −12.2911 | + | 8.16172i | −0.582653 | + | 0.386903i | ||||
\(446\) | 6.45532i | 0.305668i | ||||||||
\(447\) | −15.7162 | − | 4.66451i | −0.743353 | − | 0.220624i | ||||
\(448\) | 3.33681 | − | 3.33681i | 0.157649 | − | 0.157649i | ||||
\(449\) | −21.7175 | −1.02491 | −0.512456 | − | 0.858714i | \(-0.671264\pi\) | ||||
−0.512456 | + | 0.858714i | \(0.671264\pi\) | |||||||
\(450\) | 2.83388 | − | 14.7299i | 0.133590 | − | 0.694373i | ||||
\(451\) | 0.0120017 | 0.000565136 | ||||||||
\(452\) | 0.674324 | − | 0.674324i | 0.0317175 | − | 0.0317175i | ||||
\(453\) | 19.1651 | + | 5.68812i | 0.900456 | + | 0.267251i | ||||
\(454\) | 12.6555i | 0.593952i | ||||||||
\(455\) | −14.2848 | + | 9.48565i | −0.669684 | + | 0.444694i | ||||
\(456\) | 1.52260 | − | 0.825649i | 0.0713022 | − | 0.0386646i | ||||
\(457\) | 15.9122 | + | 15.9122i | 0.744341 | + | 0.744341i | 0.973410 | − | 0.229069i | \(-0.0735683\pi\) |
−0.229069 | + | 0.973410i | \(0.573568\pi\) | |||||||
\(458\) | −11.0578 | − | 11.0578i | −0.516696 | − | 0.516696i | ||||
\(459\) | 36.2831 | + | 2.91411i | 1.69355 | + | 0.136019i | ||||
\(460\) | −0.806715 | + | 3.99568i | −0.0376133 | + | 0.186299i | ||||
\(461\) | 38.4951i | 1.79289i | 0.443151 | + | 0.896447i | \(0.353860\pi\) | ||||
−0.443151 | + | 0.896447i | \(0.646140\pi\) | |||||||
\(462\) | −0.00767251 | + | 0.0258512i | −0.000356957 | + | 0.00120271i | ||||
\(463\) | 10.3976 | − | 10.3976i | 0.483219 | − | 0.483219i | −0.422939 | − | 0.906158i | \(-0.639002\pi\) |
0.906158 | + | 0.422939i | \(0.139002\pi\) | |||||||
\(464\) | −1.91798 | −0.0890400 | ||||||||
\(465\) | 12.9276 | − | 3.96592i | 0.599502 | − | 0.183915i | ||||
\(466\) | −16.3351 | −0.756711 | ||||||||
\(467\) | −15.9962 | + | 15.9962i | −0.740216 | + | 0.740216i | −0.972619 | − | 0.232404i | \(-0.925341\pi\) |
0.232404 | + | 0.972619i | \(0.425341\pi\) | |||||||
\(468\) | −1.00850 | − | 4.76971i | −0.0466181 | − | 0.220480i | ||||
\(469\) | 37.1469i | 1.71528i | ||||||||
\(470\) | 3.62643 | + | 5.46119i | 0.167275 | + | 0.251906i | ||||
\(471\) | 10.2948 | + | 18.9849i | 0.474359 | + | 0.874776i | ||||
\(472\) | −8.40651 | − | 8.40651i | −0.386941 | − | 0.386941i | ||||
\(473\) | 0.00501915 | + | 0.00501915i | 0.000230781 | + | 0.000230781i | ||||
\(474\) | 10.3263 | + | 19.0430i | 0.474305 | + | 0.874676i | ||||
\(475\) | −4.60834 | − | 1.93989i | −0.211445 | − | 0.0890084i | ||||
\(476\) | − | 33.0570i | − | 1.51517i | ||||||
\(477\) | 5.24577 | + | 24.8098i | 0.240187 | + | 1.13596i | ||||
\(478\) | −7.33796 | + | 7.33796i | −0.335631 | + | 0.335631i | ||||
\(479\) | 14.7942 | 0.675966 | 0.337983 | − | 0.941152i | \(-0.390255\pi\) | ||||
0.337983 | + | 0.941152i | \(0.390255\pi\) | |||||||
\(480\) | 1.81497 | − | 3.42138i | 0.0828419 | − | 0.156164i | ||||
\(481\) | −15.4258 | −0.703355 | ||||||||
\(482\) | 10.1868 | − | 10.1868i | 0.463994 | − | 0.463994i | ||||
\(483\) | 4.23948 | − | 14.2842i | 0.192903 | − | 0.649954i | ||||
\(484\) | − | 11.0000i | − | 0.500000i | ||||||
\(485\) | 23.9383 | + | 4.83307i | 1.08698 | + | 0.219458i | ||||
\(486\) | −12.3417 | − | 9.52268i | −0.559833 | − | 0.431958i | ||||
\(487\) | 10.6497 | + | 10.6497i | 0.482584 | + | 0.482584i | 0.905956 | − | 0.423372i | \(-0.139154\pi\) |
−0.423372 | + | 0.905956i | \(0.639154\pi\) | |||||||
\(488\) | 1.38120 | + | 1.38120i | 0.0625239 | + | 0.0625239i | ||||
\(489\) | −3.89646 | + | 2.11291i | −0.176204 | + | 0.0955489i | ||||
\(490\) | 33.4662 | + | 6.75672i | 1.51185 | + | 0.305238i | ||||
\(491\) | − | 18.0717i | − | 0.815564i | −0.913079 | − | 0.407782i | \(-0.866302\pi\) | ||
0.913079 | − | 0.407782i | \(-0.133698\pi\) | |||||||
\(492\) | 6.04038 | + | 1.79276i | 0.272321 | + | 0.0808237i | ||||
\(493\) | −9.50052 | + | 9.50052i | −0.427882 | + | 0.427882i | ||||
\(494\) | −1.62506 | −0.0731147 | ||||||||
\(495\) | 0.000202529 | 0.0221306i | 9.10299e−6 | 0.000994698i | ||||||
\(496\) | 3.49143 | 0.156770 | ||||||||
\(497\) | −10.7775 | + | 10.7775i | −0.483438 | + | 0.483438i | ||||
\(498\) | −21.8377 | − | 6.48134i | −0.978572 | − | 0.290436i | ||||
\(499\) | 19.9749i | 0.894200i | 0.894484 | + | 0.447100i | \(0.147543\pi\) | ||||
−0.894484 | + | 0.447100i | \(0.852457\pi\) | |||||||
\(500\) | −10.9839 | + | 2.08671i | −0.491214 | + | 0.0933205i | ||||
\(501\) | −21.9253 | + | 11.8893i | −0.979548 | + | 0.531173i | ||||
\(502\) | 14.6434 | + | 14.6434i | 0.653567 | + | 0.653567i | ||||
\(503\) | 12.9225 | + | 12.9225i | 0.576187 | + | 0.576187i | 0.933850 | − | 0.357664i | \(-0.116427\pi\) |
−0.357664 | + | 0.933850i | \(0.616427\pi\) | |||||||
\(504\) | −7.72308 | + | 11.8647i | −0.344013 | + | 0.528495i | ||||
\(505\) | −20.0225 | − | 30.1527i | −0.890989 | − | 1.34178i | ||||
\(506\) | − | 0.00601433i | − | 0.000267370i | ||||||
\(507\) | 5.10519 | − | 17.2010i | 0.226729 | − | 0.763925i | ||||
\(508\) | 0.324072 | − | 0.324072i | 0.0143783 | − | 0.0143783i | ||||
\(509\) | 19.0740 | 0.845441 | 0.422721 | − | 0.906260i | \(-0.361075\pi\) | ||||
0.422721 | + | 0.906260i | \(0.361075\pi\) | |||||||
\(510\) | −7.95719 | − | 25.9378i | −0.352350 | − | 1.14854i | ||||
\(511\) | −69.2457 | −3.06325 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −3.95659 | + | 3.36829i | −0.174688 | + | 0.148714i | ||||
\(514\) | − | 10.2440i | − | 0.451843i | ||||||
\(515\) | 0.146204 | − | 0.724153i | 0.00644253 | − | 0.0319100i | ||||
\(516\) | 1.77638 | + | 3.27586i | 0.0782006 | + | 0.144212i | ||||
\(517\) | −0.00683938 | − | 0.00683938i | −0.000300796 | − | 0.000300796i | ||||
\(518\) | 31.6745 | + | 31.6745i | 1.39170 | + | 1.39170i | ||||
\(519\) | 4.81517 | + | 8.87976i | 0.211363 | + | 0.389778i | ||||
\(520\) | −3.02712 | + | 2.01012i | −0.132748 | + | 0.0881495i | ||||
\(521\) | 20.0460i | 0.878229i | 0.898431 | + | 0.439115i | \(0.144708\pi\) | ||||
−0.898431 | + | 0.439115i | \(0.855292\pi\) | |||||||
\(522\) | 5.62948 | − | 1.19029i | 0.246396 | − | 0.0520976i | ||||
\(523\) | 7.71687 | − | 7.71687i | 0.337435 | − | 0.337435i | −0.517966 | − | 0.855401i | \(-0.673311\pi\) |
0.855401 | + | 0.517966i | \(0.173311\pi\) | |||||||
\(524\) | 15.9941 | 0.698706 | ||||||||
\(525\) | 40.6695 | − | 4.01676i | 1.77496 | − | 0.175306i | ||||
\(526\) | 2.68875 | 0.117235 | ||||||||
\(527\) | 17.2944 | − | 17.2944i | 0.753357 | − | 0.753357i | ||||
\(528\) | −0.00162589 | + | 0.00547816i | −7.07578e−5 | + | 0.000238406i | ||||
\(529\) | − | 19.6768i | − | 0.855511i | ||||||
\(530\) | 15.7457 | − | 10.4557i | 0.683948 | − | 0.454167i | ||||
\(531\) | 29.8911 | + | 19.4570i | 1.29716 | + | 0.844360i | ||||
\(532\) | 3.33681 | + | 3.33681i | 0.144669 | + | 0.144669i | ||||
\(533\) | −4.18012 | − | 4.18012i | −0.181061 | − | 0.181061i | ||||
\(534\) | 10.0465 | − | 5.44784i | 0.434754 | − | 0.235751i | ||||
\(535\) | 8.27981 | − | 41.0101i | 0.357967 | − | 1.77302i | ||||
\(536\) | 7.87184i | 0.340012i | ||||||||
\(537\) | 2.90448 | + | 0.862035i | 0.125337 | + | 0.0371996i | ||||
\(538\) | −15.1342 | + | 15.1342i | −0.652480 | + | 0.652480i | ||||
\(539\) | −0.0503736 | −0.00216975 | ||||||||
\(540\) | −3.20385 | + | 11.1685i | −0.137872 | + | 0.480616i | ||||
\(541\) | 13.4099 | 0.576536 | 0.288268 | − | 0.957550i | \(-0.406921\pi\) | ||||
0.288268 | + | 0.957550i | \(0.406921\pi\) | |||||||
\(542\) | 3.45497 | − | 3.45497i | 0.148404 | − | 0.148404i | ||||
\(543\) | 27.9904 | + | 8.30740i | 1.20118 | + | 0.356505i | ||||
\(544\) | − | 7.00516i | − | 0.300344i | ||||||
\(545\) | −19.2291 | − | 28.9579i | −0.823683 | − | 1.24042i | ||||
\(546\) | 11.6761 | − | 6.33154i | 0.499692 | − | 0.270965i | ||||
\(547\) | −6.28103 | − | 6.28103i | −0.268557 | − | 0.268557i | 0.559961 | − | 0.828519i | \(-0.310816\pi\) |
−0.828519 | + | 0.559961i | \(0.810816\pi\) | |||||||
\(548\) | −4.73854 | − | 4.73854i | −0.202420 | − | 0.202420i | ||||
\(549\) | −4.91113 | − | 3.19680i | −0.209602 | − | 0.136436i | ||||
\(550\) | 0.0152762 | − | 0.00622515i | 0.000651379 | − | 0.000265441i | ||||
\(551\) | − | 1.91798i | − | 0.0817087i | ||||||
\(552\) | 0.898394 | − | 3.02698i | 0.0382382 | − | 0.128837i | ||||
\(553\) | −41.7332 | + | 41.7332i | −1.77468 | + | 1.77468i | ||||
\(554\) | 23.5144 | 0.999031 | ||||||||
\(555\) | 32.4774 | + | 17.2286i | 1.37859 | + | 0.731312i | ||||
\(556\) | 21.0400 | 0.892294 | ||||||||
\(557\) | −0.190340 | + | 0.190340i | −0.00806496 | + | 0.00806496i | −0.711128 | − | 0.703063i | \(-0.751815\pi\) |
0.703063 | + | 0.711128i | \(0.251815\pi\) | |||||||
\(558\) | −10.2477 | + | 2.16677i | −0.433820 | + | 0.0917265i | ||||
\(559\) | − | 3.49629i | − | 0.147877i | ||||||
\(560\) | 10.3432 | + | 2.08826i | 0.437080 | + | 0.0882451i | ||||
\(561\) | 0.0190818 | + | 0.0351892i | 0.000805635 | + | 0.00148569i | ||||
\(562\) | −5.61673 | − | 5.61673i | −0.236928 | − | 0.236928i | ||||
\(563\) | 26.9104 | + | 26.9104i | 1.13414 | + | 1.13414i | 0.989482 | + | 0.144658i | \(0.0462081\pi\) |
0.144658 | + | 0.989482i | \(0.453792\pi\) | |||||||
\(564\) | −2.42059 | − | 4.46386i | −0.101925 | − | 0.187963i | ||||
\(565\) | 2.09022 | + | 0.422010i | 0.0879364 | + | 0.0177541i | ||||
\(566\) | 12.6056i | 0.529853i | ||||||||
\(567\) | 15.3049 | − | 39.6171i | 0.642744 | − | 1.66376i | ||||
\(568\) | −2.28388 | + | 2.28388i | −0.0958294 | + | 0.0958294i | ||||
\(569\) | 8.17866 | 0.342867 | 0.171434 | − | 0.985196i | \(-0.445160\pi\) | ||||
0.171434 | + | 0.985196i | \(0.445160\pi\) | |||||||
\(570\) | 3.42138 | + | 1.81497i | 0.143306 | + | 0.0760209i | ||||
\(571\) | 45.6052 | 1.90852 | 0.954259 | − | 0.298982i | \(-0.0966469\pi\) | ||||
0.954259 | + | 0.298982i | \(0.0966469\pi\) | |||||||
\(572\) | 0.00379104 | − | 0.00379104i | 0.000158512 | − | 0.000158512i | ||||
\(573\) | −1.27766 | + | 4.30484i | −0.0533749 | + | 0.179837i | ||||
\(574\) | 17.1665i | 0.716515i | ||||||||
\(575\) | −8.44094 | + | 3.43974i | −0.352011 | + | 0.143447i | ||||
\(576\) | −1.63661 | + | 2.51426i | −0.0681920 | + | 0.104761i | ||||
\(577\) | −1.91976 | − | 1.91976i | −0.0799205 | − | 0.0799205i | 0.666016 | − | 0.745937i | \(-0.267998\pi\) |
−0.745937 | + | 0.666016i | \(0.767998\pi\) | |||||||
\(578\) | −22.6785 | − | 22.6785i | −0.943303 | − | 0.943303i | ||||
\(579\) | 2.54734 | − | 1.38133i | 0.105864 | − | 0.0574062i | ||||
\(580\) | −2.37245 | − | 3.57277i | −0.0985107 | − | 0.148351i | ||||
\(581\) | − | 62.0619i | − | 2.57476i | ||||||
\(582\) | −18.1348 | − | 5.38232i | −0.751712 | − | 0.223104i | ||||
\(583\) | −0.0197193 | + | 0.0197193i | −0.000816688 | + | 0.000816688i | ||||
\(584\) | −14.6739 | −0.607212 | ||||||||
\(585\) | 7.63745 | − | 7.77853i | 0.315770 | − | 0.321603i | ||||
\(586\) | 20.8935 | 0.863104 | ||||||||
\(587\) | −26.0323 | + | 26.0323i | −1.07447 | + | 1.07447i | −0.0774740 | + | 0.996994i | \(0.524685\pi\) |
−0.996994 | + | 0.0774740i | \(0.975315\pi\) | |||||||
\(588\) | −25.3528 | − | 7.52460i | −1.04553 | − | 0.310309i | ||||
\(589\) | 3.49143i | 0.143862i | ||||||||
\(590\) | 5.26101 | − | 26.0579i | 0.216592 | − | 1.07279i | ||||
\(591\) | 16.5348 | − | 8.96620i | 0.680149 | − | 0.368820i | ||||
\(592\) | 6.71219 | + | 6.71219i | 0.275869 | + | 0.275869i | ||||
\(593\) | 11.6400 | + | 11.6400i | 0.477997 | + | 0.477997i | 0.904490 | − | 0.426494i | \(-0.140251\pi\) |
−0.426494 | + | 0.904490i | \(0.640251\pi\) | |||||||
\(594\) | 0.00137244 | − | 0.0170880i | 5.63120e−5 | − | 0.000701129i | ||||
\(595\) | 61.5780 | − | 40.8900i | 2.52445 | − | 1.67633i | ||||
\(596\) | − | 9.46498i | − | 0.387701i | ||||||
\(597\) | −4.05272 | + | 13.6549i | −0.165867 | + | 0.558860i | ||||
\(598\) | −2.09476 | + | 2.09476i | −0.0856611 | + | 0.0856611i | ||||
\(599\) | −11.6334 | −0.475328 | −0.237664 | − | 0.971347i | \(-0.576382\pi\) | ||||
−0.237664 | + | 0.971347i | \(0.576382\pi\) | |||||||
\(600\) | 8.61832 | − | 0.851196i | 0.351842 | − | 0.0347499i | ||||
\(601\) | −9.12827 | −0.372350 | −0.186175 | − | 0.982517i | \(-0.559609\pi\) | ||||
−0.186175 | + | 0.982517i | \(0.559609\pi\) | |||||||
\(602\) | −7.17911 | + | 7.17911i | −0.292599 | + | 0.292599i | ||||
\(603\) | −4.88524 | − | 23.1047i | −0.198942 | − | 0.940897i | ||||
\(604\) | 11.5421i | 0.469639i | ||||||||
\(605\) | 20.4906 | − | 13.6065i | 0.833059 | − | 0.553182i | ||||
\(606\) | 13.3647 | + | 24.6462i | 0.542905 | + | 1.00118i | ||||
\(607\) | −26.6678 | − | 26.6678i | −1.08241 | − | 1.08241i | −0.996284 | − | 0.0861303i | \(-0.972550\pi\) |
−0.0861303 | − | 0.996284i | \(-0.527450\pi\) | |||||||
\(608\) | 0.707107 | + | 0.707107i | 0.0286770 | + | 0.0286770i | ||||
\(609\) | 7.47284 | + | 13.7808i | 0.302815 | + | 0.558427i | ||||
\(610\) | −0.864390 | + | 4.28135i | −0.0349981 | + | 0.173347i | ||||
\(611\) | 4.76424i | 0.192741i | ||||||||
\(612\) | 4.34738 | + | 20.5609i | 0.175732 | + | 0.831126i | ||||
\(613\) | −11.8727 | + | 11.8727i | −0.479532 | + | 0.479532i | −0.904982 | − | 0.425450i | \(-0.860116\pi\) |
0.425450 | + | 0.904982i | \(0.360116\pi\) | |||||||
\(614\) | −28.8383 | −1.16382 | ||||||||
\(615\) | 4.13216 | + | 13.4695i | 0.166625 | + | 0.543141i | ||||
\(616\) | −0.0155687 | −0.000627280 | ||||||||
\(617\) | 24.2856 | − | 24.2856i | 0.977701 | − | 0.977701i | −0.0220560 | − | 0.999757i | \(-0.507021\pi\) |
0.999757 | + | 0.0220560i | \(0.00702122\pi\) | |||||||
\(618\) | −0.162820 | + | 0.548593i | −0.00654957 | + | 0.0220676i | ||||
\(619\) | − | 13.1124i | − | 0.527030i | −0.964655 | − | 0.263515i | \(-0.915118\pi\) | ||
0.964655 | − | 0.263515i | \(-0.0848819\pi\) | |||||||
\(620\) | 4.31873 | + | 6.50376i | 0.173444 | + | 0.261197i | ||||
\(621\) | −0.758350 | + | 9.44206i | −0.0304315 | + | 0.378897i | ||||
\(622\) | 4.44929 | + | 4.44929i | 0.178400 | + | 0.178400i | ||||
\(623\) | 22.0171 | + | 22.0171i | 0.882095 | + | 0.882095i | ||||
\(624\) | 2.47431 | − | 1.34173i | 0.0990515 | − | 0.0537120i | ||||
\(625\) | −17.4736 | − | 17.8794i | −0.698945 | − | 0.715175i | ||||
\(626\) | − | 8.40047i | − | 0.335750i | ||||||
\(627\) | −0.00547816 | − | 0.00162589i | −0.000218777 | − | 6.49318e-5i | ||||
\(628\) | −8.81673 | + | 8.81673i | −0.351826 | + | 0.351826i | ||||
\(629\) | 66.4962 | 2.65138 | ||||||||
\(630\) | −31.6544 | + | 0.289686i | −1.26114 | + | 0.0115413i | ||||
\(631\) | 38.4496 | 1.53066 | 0.765328 | − | 0.643641i | \(-0.222577\pi\) | ||||
0.765328 | + | 0.643641i | \(0.222577\pi\) | |||||||
\(632\) | −8.84374 | + | 8.84374i | −0.351785 | + | 0.351785i | ||||
\(633\) | −24.6946 | − | 7.32924i | −0.981522 | − | 0.291311i | ||||
\(634\) | 18.2484i | 0.724736i | ||||||||
\(635\) | 1.00454 | + | 0.202812i | 0.0398638 | + | 0.00804836i | ||||
\(636\) | −12.8702 | + | 6.97903i | −0.510336 | + | 0.276737i | ||||
\(637\) | 17.5449 | + | 17.5449i | 0.695154 | + | 0.695154i | ||||
\(638\) | 0.00447440 | + | 0.00447440i | 0.000177143 | + | 0.000177143i | ||||
\(639\) | 5.28606 | − | 8.12080i | 0.209113 | − | 0.321254i | ||||
\(640\) | 2.19184 | + | 0.442526i | 0.0866402 | + | 0.0174924i | ||||
\(641\) | − | 11.4967i | − | 0.454092i | −0.973884 | − | 0.227046i | \(-0.927093\pi\) | ||
0.973884 | − | 0.227046i | \(-0.0729067\pi\) | |||||||
\(642\) | −9.22077 | + | 31.0678i | −0.363915 | + | 1.22615i | ||||
\(643\) | −35.5378 | + | 35.5378i | −1.40147 | + | 1.40147i | −0.606035 | + | 0.795438i | \(0.707241\pi\) |
−0.795438 | + | 0.606035i | \(0.792759\pi\) | |||||||
\(644\) | 8.60255 | 0.338988 | ||||||||
\(645\) | −3.90490 | + | 7.36108i | −0.153755 | + | 0.289842i | ||||
\(646\) | 7.00516 | 0.275614 | ||||||||
\(647\) | −10.4682 | + | 10.4682i | −0.411548 | + | 0.411548i | −0.882278 | − | 0.470729i | \(-0.843991\pi\) |
0.470729 | + | 0.882278i | \(0.343991\pi\) | |||||||
\(648\) | 3.24328 | − | 8.39531i | 0.127408 | − | 0.329799i | ||||
\(649\) | 0.0392226i | 0.00153962i | ||||||||
\(650\) | −7.48881 | − | 3.15243i | −0.293735 | − | 0.123649i | ||||
\(651\) | −13.6033 | − | 25.0861i | −0.533155 | − | 0.983203i | ||||
\(652\) | −1.80955 | − | 1.80955i | −0.0708673 | − | 0.0708673i | ||||
\(653\) | −6.60928 | − | 6.60928i | −0.258641 | − | 0.258641i | 0.565860 | − | 0.824501i | \(-0.308544\pi\) |
−0.824501 | + | 0.565860i | \(0.808544\pi\) | |||||||
\(654\) | 12.8351 | + | 23.6696i | 0.501894 | + | 0.925554i | ||||
\(655\) | 19.7840 | + | 29.7935i | 0.773023 | + | 1.16413i | ||||
\(656\) | 3.63777i | 0.142031i | ||||||||
\(657\) | 43.0696 | − | 9.10660i | 1.68031 | − | 0.355282i | ||||
\(658\) | 9.78265 | − | 9.78265i | 0.381368 | − | 0.381368i | ||||
\(659\) | −17.5688 | −0.684382 | −0.342191 | − | 0.939630i | \(-0.611169\pi\) | ||||
−0.342191 | + | 0.939630i | \(0.611169\pi\) | |||||||
\(660\) | −0.0122158 | + | 0.00374755i | −0.000475497 | + | 0.000145873i | ||||
\(661\) | −49.5755 | −1.92826 | −0.964132 | − | 0.265422i | \(-0.914489\pi\) | ||||
−0.964132 | + | 0.265422i | \(0.914489\pi\) | |||||||
\(662\) | −15.7560 | + | 15.7560i | −0.612376 | + | 0.612376i | ||||
\(663\) | 5.61012 | − | 18.9023i | 0.217879 | − | 0.734105i | ||||
\(664\) | − | 13.1516i | − | 0.510381i | ||||||
\(665\) | −2.08826 | + | 10.3432i | −0.0809792 | + | 0.401092i | ||||
\(666\) | −23.8665 | − | 15.5354i | −0.924810 | − | 0.601986i | ||||
\(667\) | −2.47235 | − | 2.47235i | −0.0957299 | − | 0.0957299i | ||||
\(668\) | −10.1823 | − | 10.1823i | −0.393964 | − | 0.393964i | ||||
\(669\) | 9.82886 | − | 5.32983i | 0.380006 | − | 0.206063i | ||||
\(670\) | −14.6635 | + | 9.73710i | −0.566501 | + | 0.376177i | ||||
\(671\) | − | 0.00644432i | − | 0.000248780i | ||||||
\(672\) | −7.83564 | − | 2.32558i | −0.302266 | − | 0.0897113i | ||||
\(673\) | 1.10810 | − | 1.10810i | 0.0427143 | − | 0.0427143i | −0.685427 | − | 0.728141i | \(-0.740384\pi\) |
0.728141 | + | 0.685427i | \(0.240384\pi\) | |||||||
\(674\) | 26.9167 | 1.03679 | ||||||||
\(675\) | −24.7675 | + | 7.84685i | −0.953300 | + | 0.302025i | ||||
\(676\) | 10.3592 | 0.398431 | ||||||||
\(677\) | −30.2637 | + | 30.2637i | −1.16313 | + | 1.16313i | −0.179342 | + | 0.983787i | \(0.557397\pi\) |
−0.983787 | + | 0.179342i | \(0.942603\pi\) | |||||||
\(678\) | −1.58348 | − | 0.469969i | −0.0608132 | − | 0.0180491i | ||||
\(679\) | − | 51.5383i | − | 1.97786i | ||||||
\(680\) | 13.0491 | − | 8.66506i | 0.500409 | − | 0.332290i | ||||
\(681\) | 19.2692 | − | 10.4490i | 0.738398 | − | 0.400406i | ||||
\(682\) | −0.00814505 | − | 0.00814505i | −0.000311890 | − | 0.000311890i | ||||
\(683\) | 22.9904 | + | 22.9904i | 0.879703 | + | 0.879703i | 0.993504 | − | 0.113800i | \(-0.0363024\pi\) |
−0.113800 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(684\) | −2.51426 | − | 1.63661i | −0.0961352 | − | 0.0625772i | ||||
\(685\) | 2.96550 | − | 14.6882i | 0.113306 | − | 0.561207i | ||||
\(686\) | − | 39.0189i | − | 1.48975i | ||||||
\(687\) | −7.70671 | + | 25.9664i | −0.294029 | + | 0.990680i | ||||
\(688\) | −1.52133 | + | 1.52133i | −0.0580003 | + | 0.0580003i | ||||
\(689\) | 13.7362 | 0.523309 | ||||||||
\(690\) | 6.74987 | − | 2.07073i | 0.256963 | − | 0.0788312i | ||||
\(691\) | −5.79714 | −0.220534 | −0.110267 | − | 0.993902i | \(-0.535171\pi\) | ||||
−0.110267 | + | 0.993902i | \(0.535171\pi\) | |||||||
\(692\) | −4.12383 | + | 4.12383i | −0.156765 | + | 0.156765i | ||||
\(693\) | 0.0456957 | − | 0.00966186i | 0.00173584 | − | 0.000367024i | ||||
\(694\) | 3.74006i | 0.141971i | ||||||||
\(695\) | 26.0255 | + | 39.1929i | 0.987203 | + | 1.48667i | ||||
\(696\) | 1.58358 | + | 2.92031i | 0.0600254 | + | 0.110694i | ||||
\(697\) | 18.0193 | + | 18.0193i | 0.682531 | + | 0.682531i | ||||
\(698\) | 19.7371 | + | 19.7371i | 0.747059 | + | 0.747059i | ||||
\(699\) | 13.4871 | + | 24.8718i | 0.510129 | + | 0.940739i | ||||
\(700\) | 8.90409 | + | 21.8502i | 0.336543 | + | 0.825859i | ||||
\(701\) | − | 25.8432i | − | 0.976085i | −0.872820 | − | 0.488043i | \(-0.837711\pi\) | ||
0.872820 | − | 0.488043i | \(-0.162289\pi\) | |||||||
\(702\) | −6.42968 | + | 5.47365i | −0.242673 | + | 0.206590i | ||||
\(703\) | −6.71219 | + | 6.71219i | −0.253155 | + | 0.253155i | ||||
\(704\) | −0.00329918 | −0.000124342 | ||||||||
\(705\) | 5.32104 | − | 10.0306i | 0.200402 | − | 0.377775i | ||||
\(706\) | 5.14338 | 0.193574 | ||||||||
\(707\) | −54.0127 | + | 54.0127i | −2.03136 | + | 2.03136i | ||||
\(708\) | −5.85890 | + | 19.7406i | −0.220191 | + | 0.741896i | ||||
\(709\) | − | 32.2841i | − | 1.21246i | −0.795291 | − | 0.606228i | \(-0.792682\pi\) | ||
0.795291 | − | 0.606228i | \(-0.207318\pi\) | |||||||
\(710\) | −7.07941 | − | 1.42931i | −0.265686 | − | 0.0536411i | ||||
\(711\) | 20.4690 | − | 31.4457i | 0.767646 | − | 1.17931i | ||||
\(712\) | 4.66567 | + | 4.66567i | 0.174853 | + | 0.174853i | ||||
\(713\) | 4.50059 | + | 4.50059i | 0.168548 | + | 0.168548i | ||||
\(714\) | −50.3326 | + | 27.2935i | −1.88365 | + | 1.02143i | ||||
\(715\) | 0.0117512 | + | 0.00237253i | 0.000439471 | + | 8.87278e-5i | ||||
\(716\) | 1.74920i | 0.0653706i | ||||||||
\(717\) | 17.2314 | + | 5.11418i | 0.643517 | + | 0.190993i | ||||
\(718\) | 13.4372 | − | 13.4372i | 0.501473 | − | 0.501473i | ||||
\(719\) | −46.4403 | −1.73193 | −0.865965 | − | 0.500105i | \(-0.833295\pi\) | ||||
−0.865965 | + | 0.500105i | \(0.833295\pi\) | |||||||
\(720\) | −6.70792 | + | 0.0613876i | −0.249990 | + | 0.00228778i | ||||
\(721\) | −1.55908 | −0.0580630 | ||||||||
\(722\) | −0.707107 | + | 0.707107i | −0.0263158 | + | 0.0263158i | ||||
\(723\) | −23.9210 | − | 7.09964i | −0.889632 | − | 0.264039i | ||||
\(724\) | 16.8570i | 0.626485i | ||||||||
\(725\) | 3.72068 | − | 8.83871i | 0.138182 | − | 0.328261i | ||||
\(726\) | −16.7486 | + | 9.08213i | −0.621597 | + | 0.337070i | ||||
\(727\) | 24.1873 | + | 24.1873i | 0.897056 | + | 0.897056i | 0.995175 | − | 0.0981183i | \(-0.0312824\pi\) |
−0.0981183 | + | 0.995175i | \(0.531282\pi\) | |||||||
\(728\) | 5.42249 | + | 5.42249i | 0.200971 | + | 0.200971i | ||||
\(729\) | −4.30927 | + | 26.6539i | −0.159603 | + | 0.987181i | ||||
\(730\) | −18.1510 | − | 27.3343i | −0.671798 | − | 1.01169i | ||||
\(731\) | 15.0715i | 0.557441i | ||||||||
\(732\) | 0.962624 | − | 3.24339i | 0.0355796 | − | 0.119879i | ||||
\(733\) | 22.2566 | − | 22.2566i | 0.822065 | − | 0.822065i | −0.164339 | − | 0.986404i | \(-0.552549\pi\) |
0.986404 | + | 0.164339i | \(0.0525491\pi\) | |||||||
\(734\) | 4.76035 | 0.175708 | ||||||||
\(735\) | −17.3436 | − | 56.5343i | −0.639728 | − | 2.08530i | ||||
\(736\) | 1.82298 | 0.0671958 | ||||||||
\(737\) | 0.0183640 | − | 0.0183640i | 0.000676447 | − | 0.000676447i | ||||
\(738\) | −2.25759 | − | 10.6773i | −0.0831030 | − | 0.393035i | ||||
\(739\) | − | 32.3498i | − | 1.19001i | −0.803724 | − | 0.595003i | \(-0.797151\pi\) | ||
0.803724 | − | 0.595003i | \(-0.202849\pi\) | |||||||
\(740\) | −4.20066 | + | 20.8060i | −0.154419 | + | 0.764843i | ||||
\(741\) | 1.34173 | + | 2.47431i | 0.0492895 | + | 0.0908959i | ||||
\(742\) | −28.2053 | − | 28.2053i | −1.03545 | − | 1.03545i | ||||
\(743\) | 12.0657 | + | 12.0657i | 0.442649 | + | 0.442649i | 0.892901 | − | 0.450253i | \(-0.148666\pi\) |
−0.450253 | + | 0.892901i | \(0.648666\pi\) | |||||||
\(744\) | −2.88269 | − | 5.31604i | −0.105685 | − | 0.194895i | ||||
\(745\) | 17.6312 | − | 11.7077i | 0.645956 | − | 0.428938i | ||||
\(746\) | − | 6.61149i | − | 0.242064i | ||||||
\(747\) | 8.16184 | + | 38.6014i | 0.298626 | + | 1.41235i | ||||
\(748\) | −0.0163421 | + | 0.0163421i | −0.000597528 | + | 0.000597528i | ||||
\(749\) | −88.2932 | −3.22616 | ||||||||
\(750\) | 12.2461 | + | 15.0011i | 0.447163 | + | 0.547764i | ||||
\(751\) | 0.958420 | 0.0349732 | 0.0174866 | − | 0.999847i | \(-0.494434\pi\) | ||||
0.0174866 | + | 0.999847i | \(0.494434\pi\) | |||||||
\(752\) | 2.07305 | − | 2.07305i | 0.0755965 | − | 0.0755965i | ||||
\(753\) | 10.2057 | − | 34.3863i | 0.371916 | − | 1.25311i | ||||
\(754\) | − | 3.11682i | − | 0.113508i | ||||||
\(755\) | −21.5003 | + | 14.2770i | −0.782476 | + | 0.519592i | ||||
\(756\) | 24.4417 | + | 1.96306i | 0.888936 | + | 0.0713959i | ||||
\(757\) | −11.0571 | − | 11.0571i | −0.401877 | − | 0.401877i | 0.477017 | − | 0.878894i | \(-0.341718\pi\) |
−0.878894 | + | 0.477017i | \(0.841718\pi\) | |||||||
\(758\) | 4.66927 | + | 4.66927i | 0.169596 | + | 0.169596i | ||||
\(759\) | −0.00915740 | + | 0.00496572i | −0.000332393 | + | 0.000180244i | ||||
\(760\) | −0.442526 | + | 2.19184i | −0.0160521 | + | 0.0795065i | ||||
\(761\) | 45.8185i | 1.66092i | 0.557078 | + | 0.830460i | \(0.311922\pi\) | ||||
−0.557078 | + | 0.830460i | \(0.688078\pi\) | |||||||
\(762\) | −0.761000 | − | 0.225861i | −0.0275681 | − | 0.00818209i | ||||
\(763\) | −51.8724 | + | 51.8724i | −1.87791 | + | 1.87791i | ||||
\(764\) | −2.59256 | −0.0937954 | ||||||||
\(765\) | −32.9229 | + | 33.5311i | −1.19033 | + | 1.21232i | ||||
\(766\) | 20.4149 | 0.737619 | ||||||||
\(767\) | 13.6610 | − | 13.6610i | 0.493272 | − | 0.493272i | ||||
\(768\) | −1.66046 | − | 0.492817i | −0.0599167 | − | 0.0177830i | ||||
\(769\) | − | 26.0419i | − | 0.939095i | −0.882907 | − | 0.469548i | \(-0.844417\pi\) | ||
0.882907 | − | 0.469548i | \(-0.155583\pi\) | |||||||
\(770\) | −0.0192577 | − | 0.0290010i | −0.000694000 | − | 0.00104512i | ||||
\(771\) | −15.5975 | + | 8.45794i | −0.561729 | + | 0.304605i | ||||
\(772\) | 1.18301 | + | 1.18301i | 0.0425774 | + | 0.0425774i | ||||
\(773\) | −7.42336 | − | 7.42336i | −0.267000 | − | 0.267000i | 0.560890 | − | 0.827890i | \(-0.310459\pi\) |
−0.827890 | + | 0.560890i | \(0.810459\pi\) | |||||||
\(774\) | 3.52115 | − | 5.40941i | 0.126565 | − | 0.194437i | ||||
\(775\) | −6.77299 | + | 16.0897i | −0.243293 | + | 0.577958i | ||||
\(776\) | − | 10.9215i | − | 0.392061i | ||||||
\(777\) | 22.0755 | − | 74.3795i | 0.791954 | − | 2.66835i | ||||
\(778\) | −0.400347 | + | 0.400347i | −0.0143531 | + | 0.0143531i | ||||
\(779\) | −3.63777 | −0.130337 | ||||||||
\(780\) | 5.55994 | + | 2.94943i | 0.199078 | + | 0.105607i | ||||
\(781\) | 0.0106560 | 0.000381301 | ||||||||
\(782\) | 9.02993 | − | 9.02993i | 0.322910 | − | 0.322910i | ||||
\(783\) | −6.46031 | − | 7.58867i | −0.230873 | − | 0.271197i | ||||
\(784\) | − | 15.2685i | − | 0.545305i | ||||||
\(785\) | −27.3295 | − | 5.51774i | −0.975432 | − | 0.196937i | ||||
\(786\) | −13.2055 | − | 24.3526i | −0.471025 | − | 0.868628i | ||||
\(787\) | 16.1249 | + | 16.1249i | 0.574791 | + | 0.574791i | 0.933464 | − | 0.358672i | \(-0.116770\pi\) |
−0.358672 | + | 0.933464i | \(0.616770\pi\) | |||||||
\(788\) | 7.67888 | + | 7.67888i | 0.273549 | + | 0.273549i | ||||
\(789\) | −2.21996 | − | 4.09388i | −0.0790327 | − | 0.145746i | ||||
\(790\) | −27.4132 | − | 5.53465i | −0.975319 | − | 0.196914i | ||||
\(791\) | − | 4.50018i | − | 0.160008i | ||||||
\(792\) | 0.00968345 | − | 0.00204746i | 0.000344086 | − | 7.27532e-5i | ||||
\(793\) | −2.24452 | + | 2.24452i | −0.0797054 | + | 0.0797054i | ||||
\(794\) | 15.5947 | 0.553436 | ||||||||
\(795\) | −28.9202 | − | 15.3416i | −1.02569 | − | 0.544110i | ||||
\(796\) | −8.22358 | −0.291477 | ||||||||
\(797\) | 0.0667197 | − | 0.0667197i | 0.00236333 | − | 0.00236333i | −0.705924 | − | 0.708287i | \(-0.749468\pi\) |
0.708287 | + | 0.705924i | \(0.249468\pi\) | |||||||
\(798\) | 2.32558 | − | 7.83564i | 0.0823247 | − | 0.277379i | ||||
\(799\) | − | 20.5373i | − | 0.726559i | ||||||
\(800\) | 1.88688 | + | 4.63030i | 0.0667112 | + | 0.163706i | ||||
\(801\) | −16.5897 | − | 10.7987i | −0.586169 | − | 0.381555i | ||||
\(802\) | −23.3989 | − | 23.3989i | −0.826243 | − | 0.826243i | ||||
\(803\) | 0.0342324 | + | 0.0342324i | 0.00120804 | + | 0.00120804i | ||||
\(804\) | 11.9857 | − | 6.49938i | 0.422701 | − | 0.229215i | ||||
\(805\) | 10.6410 | + | 16.0247i | 0.375044 | + | 0.564795i | ||||
\(806\) | 5.67376i | 0.199850i | ||||||||
\(807\) | 35.5387 | + | 10.5477i | 1.25102 | + | 0.371298i | ||||
\(808\) | −11.4459 | + | 11.4459i | −0.402665 | + | 0.402665i | ||||
\(809\) | 2.41703 | 0.0849783 | 0.0424892 | − | 0.999097i | \(-0.486471\pi\) | ||||
0.0424892 | + | 0.999097i | \(0.486471\pi\) | |||||||
\(810\) | 19.6504 | − | 4.34309i | 0.690444 | − | 0.152601i | ||||
\(811\) | 5.82179 | 0.204431 | 0.102215 | − | 0.994762i | \(-0.467407\pi\) | ||||
0.102215 | + | 0.994762i | \(0.467407\pi\) | |||||||
\(812\) | −6.39993 | + | 6.39993i | −0.224593 | + | 0.224593i | ||||
\(813\) | −8.11312 | − | 2.40794i | −0.284540 | − | 0.0844500i | ||||
\(814\) | − | 0.0313173i | − | 0.00109767i | ||||||
\(815\) | 1.13246 | − | 5.60911i | 0.0396684 | − | 0.196479i | ||||
\(816\) | −10.6660 | + | 5.78381i | −0.373386 | + | 0.202474i | ||||
\(817\) | −1.52133 | − | 1.52133i | −0.0532247 | − | 0.0532247i | ||||
\(818\) | −18.5455 | − | 18.5455i | −0.648430 | − | 0.648430i | ||||
\(819\) | −19.2808 | − | 12.5504i | −0.673725 | − | 0.438547i | ||||
\(820\) | −6.77637 | + | 4.49975i | −0.236641 | + | 0.157138i | ||||
\(821\) | 5.24603i | 0.183088i | 0.995801 | + | 0.0915438i | \(0.0291802\pi\) | ||||
−0.995801 | + | 0.0915438i | \(0.970820\pi\) | |||||||
\(822\) | −3.30252 | + | 11.1273i | −0.115189 | + | 0.388108i | ||||
\(823\) | −1.84676 | + | 1.84676i | −0.0643738 | + | 0.0643738i | −0.738561 | − | 0.674187i | \(-0.764494\pi\) |
0.674187 | + | 0.738561i | \(0.264494\pi\) | |||||||
\(824\) | −0.330386 | −0.0115095 | ||||||||
\(825\) | −0.0220912 | − | 0.0181197i | −0.000769116 | − | 0.000630847i | ||||
\(826\) | −56.1018 | −1.95203 | ||||||||
\(827\) | 24.7201 | − | 24.7201i | 0.859602 | − | 0.859602i | −0.131689 | − | 0.991291i | \(-0.542040\pi\) |
0.991291 | + | 0.131689i | \(0.0420400\pi\) | |||||||
\(828\) | −5.35064 | + | 1.13133i | −0.185947 | + | 0.0393165i | ||||
\(829\) | 4.44183i | 0.154271i | 0.997021 | + | 0.0771356i | \(0.0245774\pi\) | ||||
−0.997021 | + | 0.0771356i | \(0.975423\pi\) | |||||||
\(830\) | 24.4985 | − | 16.2679i | 0.850357 | − | 0.564668i | ||||
\(831\) | −19.4146 | − | 35.8029i | −0.673486 | − | 1.24199i | ||||
\(832\) | 1.14909 | + | 1.14909i | 0.0398374 | + | 0.0398374i | ||||
\(833\) | −75.6311 | − | 75.6311i | −2.62046 | − | 2.62046i | ||||
\(834\) | −17.3716 | − | 32.0354i | −0.601531 | − | 1.10930i | ||||
\(835\) | 6.37233 | − | 31.5623i | 0.220524 | − | 1.09226i | ||||
\(836\) | − | 0.00329918i | − | 0.000114104i | ||||||
\(837\) | 11.7601 | + | 13.8142i | 0.406489 | + | 0.477487i | ||||
\(838\) | 11.8382 | − | 11.8382i | 0.408944 | − | 0.408944i | ||||
\(839\) | 21.2177 | 0.732517 | 0.366258 | − | 0.930513i | \(-0.380639\pi\) | ||||
0.366258 | + | 0.930513i | \(0.380639\pi\) | |||||||
\(840\) | −5.36028 | − | 17.4727i | −0.184947 | − | 0.602866i | ||||
\(841\) | −25.3214 | −0.873150 | ||||||||
\(842\) | 14.3887 | − | 14.3887i | 0.495867 | − | 0.495867i | ||||
\(843\) | −3.91457 | + | 13.1895i | −0.134825 | + | 0.454270i | ||||
\(844\) | − | 14.8721i | − | 0.511920i | ||||||
\(845\) | 12.8138 | + | 19.2969i | 0.440810 | + | 0.663833i | ||||
\(846\) | −4.79811 | + | 7.37117i | −0.164962 | + | 0.253426i | ||||
\(847\) | −36.7048 | − | 36.7048i | −1.26119 | − | 1.26119i | ||||
\(848\) | −5.97702 | − | 5.97702i | −0.205252 | − | 0.205252i | ||||
\(849\) | 19.1933 | − | 10.4078i | 0.658711 | − | 0.357195i | ||||
\(850\) | 32.2822 | + | 13.5893i | 1.10727 | + | 0.466108i | ||||
\(851\) | 17.3045i | 0.593192i | ||||||||
\(852\) | 5.36311 | + | 1.59175i | 0.183737 | + | 0.0545323i | ||||
\(853\) | −2.75570 | + | 2.75570i | −0.0943535 | + | 0.0943535i | −0.752708 | − | 0.658354i | \(-0.771253\pi\) |
0.658354 | + | 0.752708i | \(0.271253\pi\) | |||||||
\(854\) | 9.21758 | 0.315419 | ||||||||
\(855\) | −0.0613876 | − | 6.70792i | −0.00209941 | − | 0.229406i | ||||
\(856\) | −18.7103 | −0.639506 | ||||||||
\(857\) | −22.6298 | + | 22.6298i | −0.773020 | + | 0.773020i | −0.978633 | − | 0.205613i | \(-0.934081\pi\) |
0.205613 | + | 0.978633i | \(0.434081\pi\) | |||||||
\(858\) | −0.00890231 | − | 0.00264216i | −0.000303920 | − | 9.02020e-5i | ||||
\(859\) | 14.0009i | 0.477705i | 0.971056 | + | 0.238853i | \(0.0767713\pi\) | ||||
−0.971056 | + | 0.238853i | \(0.923229\pi\) | |||||||
\(860\) | −4.71573 | − | 0.952091i | −0.160805 | − | 0.0324660i | ||||
\(861\) | 26.1377 | − | 14.1735i | 0.890769 | − | 0.483031i | ||||
\(862\) | −26.7467 | − | 26.7467i | −0.910995 | − | 0.910995i | ||||
\(863\) | 37.8370 | + | 37.8370i | 1.28799 | + | 1.28799i | 0.936009 | + | 0.351976i | \(0.114490\pi\) |
0.351976 | + | 0.936009i | \(0.385510\pi\) | |||||||
\(864\) | 5.17947 | + | 0.415995i | 0.176209 | + | 0.0141524i | ||||
\(865\) | −12.7828 | − | 2.58080i | −0.434628 | − | 0.0877499i | ||||
\(866\) | − | 5.28008i | − | 0.179424i | ||||||
\(867\) | −15.8058 | + | 53.2548i | −0.536792 | + | 1.80863i | ||||
\(868\) | 11.6502 | − | 11.6502i | 0.395434 | − | 0.395434i | ||||
\(869\) | 0.0412626 | 0.00139974 | ||||||||
\(870\) | −3.48108 | + | 6.56215i | −0.118020 | + | 0.222478i | ||||
\(871\) | −12.7922 | −0.433446 | ||||||||
\(872\) | −10.9923 | + | 10.9923i | −0.372248 | + | 0.372248i | ||||
\(873\) | 6.77787 | + | 32.0559i | 0.229396 | + | 1.08493i | ||||
\(874\) | 1.82298i | 0.0616631i | ||||||||
\(875\) | −29.6881 | + | 43.6140i | −1.00364 | + | 1.47442i | ||||
\(876\) | 12.1155 | + | 22.3425i | 0.409346 | + | 0.754884i | ||||
\(877\) | 27.3198 | + | 27.3198i | 0.922525 | + | 0.922525i | 0.997207 | − | 0.0746821i | \(-0.0237942\pi\) |
−0.0746821 | + | 0.997207i | \(0.523794\pi\) | |||||||
\(878\) | 6.92986 | + | 6.92986i | 0.233871 | + | 0.233871i | ||||
\(879\) | −17.2507 | − | 31.8125i | −0.581853 | − | 1.07301i | ||||
\(880\) | −0.00408093 | − | 0.00614564i | −0.000137568 | − | 0.000207170i | ||||
\(881\) | 5.66516i | 0.190864i | 0.995436 | + | 0.0954321i | \(0.0304233\pi\) | ||||
−0.995436 | + | 0.0954321i | \(0.969577\pi\) | |||||||
\(882\) | 9.47560 | + | 44.8148i | 0.319060 | + | 1.50899i | ||||
\(883\) | −27.0837 | + | 27.0837i | −0.911439 | + | 0.911439i | −0.996385 | − | 0.0849469i | \(-0.972928\pi\) |
0.0849469 | + | 0.996385i | \(0.472928\pi\) | |||||||
\(884\) | 11.3838 | 0.382878 | ||||||||
\(885\) | −44.0195 | + | 13.5043i | −1.47970 | + | 0.453942i | ||||
\(886\) | −10.5674 | −0.355020 | ||||||||
\(887\) | 9.96724 | − | 9.96724i | 0.334667 | − | 0.334667i | −0.519689 | − | 0.854356i | \(-0.673952\pi\) |
0.854356 | + | 0.519689i | \(0.173952\pi\) | |||||||
\(888\) | 4.67805 | − | 15.7619i | 0.156985 | − | 0.528934i | ||||
\(889\) | − | 2.16273i | − | 0.0725355i | ||||||
\(890\) | −2.91990 | + | 14.4623i | −0.0978751 | + | 0.484778i | ||||
\(891\) | −0.0271513 | + | 0.0120190i | −0.000909603 | + | 0.000402652i | ||||
\(892\) | 4.56460 | + | 4.56460i | 0.152834 | + | 0.152834i | ||||
\(893\) | 2.07305 | + | 2.07305i | 0.0693721 | + | 0.0693721i | ||||
\(894\) | −14.4114 | + | 7.81476i | −0.481988 | + | 0.261365i | ||||
\(895\) | −3.25837 | + | 2.16368i | −0.108915 | + | 0.0723238i | ||||
\(896\) | − | 4.71896i | − | 0.157649i | ||||||
\(897\) | 4.91902 | + | 1.45994i | 0.164241 | + | 0.0487460i | ||||
\(898\) | −15.3566 | + | 15.3566i | −0.512456 | + | 0.512456i | ||||
\(899\) | −6.69649 | −0.223340 | ||||||||
\(900\) | −8.41174 | − | 12.4194i | −0.280391 | − | 0.413982i | ||||
\(901\) | −59.2131 | −1.97268 | ||||||||
\(902\) | 0.00848646 | − | 0.00848646i | 0.000282568 | − | 0.000282568i | ||||
\(903\) | 16.8583 | + | 5.00347i | 0.561010 | + | 0.166505i | ||||
\(904\) | − | 0.953638i | − | 0.0317175i | ||||||
\(905\) | −31.4008 | + | 20.8513i | −1.04380 | + | 0.693120i | ||||
\(906\) | 17.5739 | − | 9.52968i | 0.583854 | − | 0.316603i | ||||
\(907\) | −24.3414 | − | 24.3414i | −0.808242 | − | 0.808242i | 0.176126 | − | 0.984368i | \(-0.443643\pi\) |
−0.984368 | + | 0.176126i | \(0.943643\pi\) | |||||||
\(908\) | 8.94878 | + | 8.94878i | 0.296976 | + | 0.296976i | ||||
\(909\) | 26.4917 | − | 40.6982i | 0.878673 | − | 1.34987i | ||||
\(910\) | −3.39354 | + | 16.8083i | −0.112495 | + | 0.557189i | ||||
\(911\) | − | 24.6576i | − | 0.816944i | −0.912771 | − | 0.408472i | \(-0.866062\pi\) | ||
0.912771 | − | 0.408472i | \(-0.133938\pi\) | |||||||
\(912\) | 0.492817 | − | 1.66046i | 0.0163188 | − | 0.0549834i | ||||
\(913\) | −0.0306810 | + | 0.0306810i | −0.00101539 | + | 0.00101539i | ||||
\(914\) | 22.5032 | 0.744341 | ||||||||
\(915\) | 7.23245 | − | 2.21877i | 0.239097 | − | 0.0733503i | ||||
\(916\) | −15.6381 | −0.516696 | ||||||||
\(917\) | 53.3692 | − | 53.3692i | 1.76241 | − | 1.76241i | ||||
\(918\) | 27.7166 | − | 23.5954i | 0.914784 | − | 0.778764i | ||||
\(919\) | − | 39.8544i | − | 1.31468i | −0.753596 | − | 0.657338i | \(-0.771682\pi\) | ||
0.753596 | − | 0.657338i | \(-0.228318\pi\) | |||||||
\(920\) | 2.25494 | + | 3.39580i | 0.0743431 | + | 0.111956i | ||||
\(921\) | 23.8103 | + | 43.9092i | 0.784577 | + | 1.44686i | ||||
\(922\) | 27.2201 | + | 27.2201i | 0.896447 | + | 0.896447i | ||||
\(923\) | −3.71143 | − | 3.71143i | −0.122163 | − | 0.122163i | ||||
\(924\) | 0.0128543 | + | 0.0237048i | 0.000422874 | + | 0.000779832i | ||||
\(925\) | −43.9530 | + | 17.9111i | −1.44516 | + | 0.588914i | ||||
\(926\) | − | 14.7045i | − | 0.483219i | ||||||
\(927\) | 0.969718 | − | 0.205036i | 0.0318497 | − | 0.00673427i | ||||
\(928\) | −1.35622 | + | 1.35622i | −0.0445200 | + | 0.0445200i | ||||
\(929\) | 13.8105 | 0.453109 | 0.226555 | − | 0.973998i | \(-0.427254\pi\) | ||||
0.226555 | + | 0.973998i | \(0.427254\pi\) | |||||||
\(930\) | 6.33685 | − | 11.9455i | 0.207793 | − | 0.391709i | ||||
\(931\) | 15.2685 | 0.500406 | ||||||||
\(932\) | −11.5507 | + | 11.5507i | −0.378355 | + | 0.378355i | ||||
\(933\) | 3.10092 | − | 10.4480i | 0.101520 | − | 0.342053i | ||||
\(934\) | 22.6220i | 0.740216i | ||||||||
\(935\) | −0.0506563 | − | 0.0102273i | −0.00165664 | − | 0.000334470i | ||||
\(936\) | −4.08582 | − | 2.65958i | −0.133549 | − | 0.0869310i | ||||
\(937\) | −33.2655 | − | 33.2655i | −1.08674 | − | 1.08674i | −0.995863 | − | 0.0908728i | \(-0.971034\pi\) |
−0.0908728 | − | 0.995863i | \(-0.528966\pi\) | |||||||
\(938\) | 26.2668 | + | 26.2668i | 0.857642 | + | 0.857642i | ||||
\(939\) | −12.7905 | + | 6.93584i | −0.417403 | + | 0.226343i | ||||
\(940\) | 6.42592 | + | 1.29737i | 0.209590 | + | 0.0423156i | ||||
\(941\) | − | 8.74362i | − | 0.285034i | −0.989792 | − | 0.142517i | \(-0.954480\pi\) | ||
0.989792 | − | 0.142517i | \(-0.0455196\pi\) | |||||||
\(942\) | 20.7039 | + | 6.14480i | 0.674568 | + | 0.200209i | ||||
\(943\) | −4.68923 | + | 4.68923i | −0.152702 | + | 0.152702i | ||||
\(944\) | −11.8886 | −0.386941 | ||||||||
\(945\) | 26.5765 | + | 47.9577i | 0.864533 | + | 1.56006i | ||||
\(946\) | 0.00709815 | 0.000230781 | ||||||||
\(947\) | −28.7624 | + | 28.7624i | −0.934651 | + | 0.934651i | −0.997992 | − | 0.0633409i | \(-0.979824\pi\) |
0.0633409 | + | 0.997992i | \(0.479824\pi\) | |||||||
\(948\) | 20.7673 | + | 6.16363i | 0.674490 | + | 0.200186i | ||||
\(949\) | − | 23.8460i | − | 0.774073i | ||||||
\(950\) | −4.63030 | + | 1.88688i | −0.150227 | + | 0.0612184i | ||||
\(951\) | 27.7850 | − | 15.0668i | 0.900989 | − | 0.488574i | ||||
\(952\) | −23.3749 | − | 23.3749i | −0.757584 | − | 0.757584i | ||||
\(953\) | 10.3155 | + | 10.3155i | 0.334151 | + | 0.334151i | 0.854160 | − | 0.520010i | \(-0.174072\pi\) |
−0.520010 | + | 0.854160i | \(0.674072\pi\) | |||||||
\(954\) | 21.2525 | + | 13.8339i | 0.688076 | + | 0.447889i | ||||
\(955\) | −3.20687 | − | 4.82936i | −0.103772 | − | 0.156275i | ||||
\(956\) | 10.3774i | 0.335631i | ||||||||
\(957\) | 0.00311843 | − | 0.0105070i | 0.000100804 | − | 0.000339643i | ||||
\(958\) | 10.4611 | − | 10.4611i | 0.337983 | − | 0.337983i | ||||
\(959\) | −31.6232 | −1.02117 | ||||||||
\(960\) | −1.13590 | − | 3.70266i | −0.0366611 | − | 0.119503i | ||||
\(961\) | −18.8099 | −0.606772 | ||||||||
\(962\) | −10.9077 | + | 10.9077i | −0.351677 | + | 0.351677i | ||||
\(963\) | 54.9169 | − | 11.6116i | 1.76967 | − | 0.374177i | ||||
\(964\) | − | 14.4062i | − | 0.463994i | ||||||
\(965\) | −0.740357 | + | 3.66701i | −0.0238329 | + | 0.118045i | ||||
\(966\) | −7.10269 | − | 13.0982i | −0.228525 | − | 0.421428i | ||||
\(967\) | 23.9335 | + | 23.9335i | 0.769650 | + | 0.769650i | 0.978045 | − | 0.208394i | \(-0.0668238\pi\) |
−0.208394 | + | 0.978045i | \(0.566824\pi\) | |||||||
\(968\) | −7.77817 | − | 7.77817i | −0.250000 | − | 0.250000i | ||||
\(969\) | −5.78381 | − | 10.6660i | −0.185803 | − | 0.342643i | ||||
\(970\) | 20.3444 | − | 13.5094i | 0.653220 | − | 0.433762i | ||||
\(971\) | 2.91801i | 0.0936433i | 0.998903 | + | 0.0468217i | \(0.0149093\pi\) | ||||
−0.998903 | + | 0.0468217i | \(0.985091\pi\) | |||||||
\(972\) | −15.4605 | + | 1.99337i | −0.495895 | + | 0.0639374i | ||||
\(973\) | 70.2063 | − | 70.2063i | 2.25071 | − | 2.25071i | ||||
\(974\) | 15.0609 | 0.482584 | ||||||||
\(975\) | 1.38324 | + | 14.0052i | 0.0442992 | + | 0.448527i | ||||
\(976\) | 1.95331 | 0.0625239 | ||||||||
\(977\) | 9.00845 | − | 9.00845i | 0.288206 | − | 0.288206i | −0.548165 | − | 0.836370i | \(-0.684673\pi\) |
0.836370 | + | 0.548165i | \(0.184673\pi\) | |||||||
\(978\) | −1.26116 | + | 4.24926i | −0.0403275 | + | 0.135876i | ||||
\(979\) | − | 0.0217688i | − | 0.000695734i | ||||||
\(980\) | 28.4419 | − | 18.8865i | 0.908544 | − | 0.603306i | ||||
\(981\) | 25.4419 | − | 39.0855i | 0.812298 | − | 1.24790i | ||||
\(982\) | −12.7786 | − | 12.7786i | −0.407782 | − | 0.407782i | ||||
\(983\) | −6.78318 | − | 6.78318i | −0.216350 | − | 0.216350i | 0.590608 | − | 0.806958i | \(-0.298888\pi\) |
−0.806958 | + | 0.590608i | \(0.798888\pi\) | |||||||
\(984\) | 5.53886 | − | 3.00352i | 0.176573 | − | 0.0957488i | ||||
\(985\) | −4.80564 | + | 23.8025i | −0.153120 | + | 0.758410i | ||||
\(986\) | 13.4358i | 0.427882i | ||||||||
\(987\) | −22.9721 | − | 6.81801i | −0.731210 | − | 0.217020i | ||||
\(988\) | −1.14909 | + | 1.14909i | −0.0365573 | + | 0.0365573i | ||||
\(989\) | −3.92212 | −0.124716 | ||||||||
\(990\) | 0.0157919 | + | 0.0155055i | 0.000501901 | + | 0.000492798i | ||||
\(991\) | 25.2666 | 0.802619 | 0.401309 | − | 0.915943i | \(-0.368555\pi\) | ||||
0.401309 | + | 0.915943i | \(0.368555\pi\) | |||||||
\(992\) | 2.46881 | − | 2.46881i | 0.0783848 | − | 0.0783848i | ||||
\(993\) | 36.9991 | + | 10.9811i | 1.17413 | + | 0.348476i | ||||
\(994\) | 15.2417i | 0.483438i | ||||||||
\(995\) | −10.1722 | − | 15.3187i | −0.322480 | − | 0.485636i | ||||
\(996\) | −20.0246 | + | 10.8586i | −0.634504 | + | 0.344068i | ||||
\(997\) | −31.5798 | − | 31.5798i | −1.00014 | − | 1.00014i | −1.00000 | 0.000142894i | \(-0.999955\pi\) | |
−0.000142894 | − | 1.00000i | \(-0.500045\pi\) | |||||||
\(998\) | 14.1244 | + | 14.1244i | 0.447100 | + | 0.447100i | ||||
\(999\) | −3.94882 | + | 49.1660i | −0.124935 | + | 1.55554i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.2.k.b.77.10 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.77.5 | ✓ | 36 | |
5.3 | odd | 4 | inner | 570.2.k.b.533.5 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.b.533.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.5 | ✓ | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.77.10 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.533.5 | yes | 36 | 5.3 | odd | 4 | inner | |
570.2.k.b.533.10 | yes | 36 | 15.8 | even | 4 | inner |